tracer:ull - 2003 barcelona, october 25th, 2003 tracer.ull.es tic2002-04498-c05-05

Advanced Optimization Techniques for Complex Problems Tcnicas de Optimizacin Avanzadas para Problemas ComplejosTRACER:ULL - 2003

Barcelona, October 25th, 2003

http://www.tracer.ull.es

TIC2002-04498-C05-05

University of La Laguna

OutlineObjectivesResearchersProblemsBranch and Bound and Divide and Conquer SkeletonsKnapsack ProblemMatrix ProductConstrained two-dimensional cutting stock problemCALL and LLAC: tools for Complexity AnalysisSymbolic regression ProblemAn analytical model for Pipeline and Master-Slave algorithms over heterogeneous clustersResource allocation problemPrediction of the RNA Secondary Structure problemResults

TRACER::ULL ObjectivesThe TRACER::ULL main objective is to achieve an efficient resolution of the following complex problems by developing new optimization procedures:Constrained two-dimensional cutting stock problemSymbolic regression problemPrediction of the RNA secondary structure problemWe propose the design, implementation and evaluation of solving tools using exact techniques:Divide and Conquer Branch and Bound Dynamic ProgrammingIt is an objective to provide sequential, parallel and distributed implementations for academia problems:Resource allocation problemKnapsack problemMatrix ProductA second research track is related with the building of a methodology and the associated tool for the complexity and performance analysis of both sequential and parallel algorithms.Another goal is the implementation ofAn Internet execution systemsA Problem repositoryPerformance AnalysisWeb site: http://www.tracer.ull.es

ResearchersULL StaffCoromoto Len HernndezIsabel Dorta GonzlezDaniel Gonzlez MoralesCasiano Rodrguez LenJess Alberto Gonzlez MartnezForeingRumen AndonovStudentsJuan Ramn Gonzlez GonzlezGara Miranda ValladaresMara Dolores Medina Barroso

GrantsBranch and BoundDynamic ProgrammingPerformance Analysis ToolsandSymbolic regression problemDivide and Conquertwo dimensional cutting stock problemPrediction of the RNA secondary structure problem

Shared Memory Branch and Bound Skeletons// shared variables {bqueue, bstemp, soltemp, data} // private variables {auxSol, high, low} // the initial subproblem is already inserted in the global shared queue while(!bqueue.empty()) { nn = bqueue.getNumberOfNodes(); nt = (nn > maxthread)?maxthread:nn; data = new SubProblem[nt]; for (int j = 0; j < nt; j++) data[j] = bqueue.remove(); set.num.threads(nt); parallel forall (i = 0; i < nt; i++) { high = data[i].upper_bound(pbm,auxSol); if ( high > bstemp ) { low = data[i].lower_bound(pbm,auxSol); if ( low > bstemp ) { // critical region // only one thread can change the value at any time bstemp = low; soltemp = auxSol; } if ( high != low ) { // critical region // just one thread can insert subproblems in the queue at any time data[i].branch(pbm,bqueue); } } } }bestSol = bstemp;sol = soltemp;

0-1 Knapsack ProblemThe 0/1 Knapsack Problem can be stated as follows:

"We have been provided with a knapsack of capacity C and with a set of N objects; p[k] and w[k] are the profit and weight associated to object k. Without exceeding the capacity of the knapsack, the objects must be inserted into the knapsack providing the maximum profit". Martello, S., Toth, P. : Knapsack Problems Algorithms and Computer Implementatios. John Wiley & Sons Ltd. (1990)

Comparison between MPI and OpenMP skeletonsOrigin 3000- CIEMAT

Distributed Branch and Bound skeletonInitialization PhaseResolution PhaseConditional CommunicationMessage ReceptionAvoiding starvationComputeBest bound PropagationWork queryingEnding resolution phaseSolution Building

Distributed Branch and Bound skeleton


Grfico3

1.85462562041.81391680921.83427121481.8107320389

2.66282361762.58518007033.03875658592.5422060483

3.25238061693.10915146134.08869679533.1438695605

3.68530961644.6123264595

4.2342436156

4.6189117154

ULL 500 Mhz

ULL 800 Mhz

ULL 800-500 Mhz

ULL 1400 Mhz

number of processors

speedup

Knapsack N = 50.000 ULL

Sequential

89

50000

run18989

Problema:50000100000

Computednodes:2614392750821.8784182653.43164063

1639893780Sequential623971637800747.323883052608.43508913

1639893780623971637500006996.1347665002850.596435571546.03527857

run21400429.94886781234.27526861

Problema:

Computednodes:2614392

1639893780Sequential623971637

163989378062397163750000821.878418

beowulf5

run1

Problema:


1639893780Sequential623971637

163989378062397163750000747.8862305

run2

Problema:


1639893780Sequential623971637

163989378062397163750000746.7615356

beowulf8

run1

Problema:


1639893780Sequential623971637

1639893780623971637500002850.368164

run2

Problema:


1639893780Sequential623971637

1639893780623971637500002850.824707

beowulf16

run1

Problema:


1639893780Sequential623971637

163989378062397163750000437.1088867

run2

Problema:


1639893780Sequential623971637

163989378062397163750000422.7888489

89

100000

beowulf0

run1

Problema:


6562332564Sequential2499610869

65623325642499610873100000651.1342163

run2

Problema:


6562332564Sequential2499610869

65623325642499610873100000655.7290649

beowulf5

run1

Problema:


6562332564Sequential2499610869

65623325642499610873100000608.3323364

run2

Problema:


6562332564Sequential2499610869

65623325642499610873100000608.5378418

beowulf8

run1

Problema:


6562332564Sequential2499610869

656233256424996108731000001546.311768

run2

Problema:


6562332564Sequential2499610869

656233256424996108731000001545.758789

beowulf16

run1

Problema:


6562332564Sequential2499610869

65623325642499610873100000230.1702271

run2

Problema:


6562332564Sequential2499610869

65623325642499610873100000238.3803101

107

50000

beowulf0

run1

Problema:


1641207946Sequential628145372

16412079466281453755000082.7580719

run2

Problema:


1641207946Sequential628145372

16412079466281453755000082.42076111

beowulf5

run1

Problema:


1641207946Sequential628145372

16412079466281453755000081.75357819

run2

Problema:


1641207946Sequential628145372

16412079466281453755000081.58392334

beowulf8

run1

Problema:


1641207946Sequential628145372

164120794662814537550000239.3715057

run2

Problema:


1641207946Sequential628145372

164120794662814537550000238.8070831

beowulf16

run1

Problema:


1641207946Sequential628145372

16412079466281453755000033.86289597

run2

Problema:


1641207946Sequential628145372

16412079466281453755000033.95829773

107

100000

beowulf0

run1

Problema:


6569265691Sequential2510207120

65692656912510207122100000629.5508423

run2

Problema:


6569265691Sequential2510207120

65692656912510207122100000626.1575928

beowulf5

run1

Problema:


6569265691Sequential2510207120

65692656912510207122100000585.0124512

run2

Problema:


6569265691Sequential2510207120

65692656912510207122100000575.9658813

beowulf8

run1

Problema:


6569265691Sequential2510207120

656926569125102071221000001455.44397

run2

Problema:


6569265691Sequential2510207120

656926569125102071221000001429.06665

beowulf16

run1

Problema:


6569265691Sequential2510207120

65692656912510207122100000211.1840057

run2

Problema:


6569265691Sequential2510207120

65692656912510207122100000215.8686676

127

50000

beowulf0

run1

Problema:


1639547063Sequential623661898

163954706362366190050000435.9469299

run2

Problema:


1639547063Sequential623661898

163954706362366190050000437.7729187

beowulf5

run1

Problema:


1639547063Sequential623661898

163954706362366190050000425.9438477

run2

Problema:


1639547063Sequential623661898

163954706362366190050000422.4737549

beowulf8

run1

Problema:


1639547063Sequential623661898

1639547063623661900500001428.572632

run2

Problema:


1639547063Sequential623661898

1639547063623661900500001413.713501

beowulf16

run1

Problema:


1639547063Sequential623661898

163954706362366190050000204.9870148

run2

Problema:


1639547063Sequential623661898

163954706362366190050000215.970047

127

100000

beowulf0

run1

Problema:


6567126329Sequential2496892260

656712632924968922601000001550.543457

run2

Problema:


6567126329Sequential2496892260

656712632924968922601000001543.898315

beowulf5

run1

Problema:


6567126329Sequential2496892260

656712632924968922601000001448.219482

run2

Problema:


6567126329Sequential2496892260

656712632924968922601000001448.633545

beowulf8

run1

Problema:


6567126329Sequential2496892260

656712632924968922601000003613.065186

run2

Problema:


6567126329Sequential2496892260

656712632924968922601000003658.391113

beowulf16

run1

Problema:


6567126329Sequential2496892260

65671263292496892260100000531.3937988

run2

Problema:


6567126329Sequential2496892260

65671263292496892260100000558.8529663

607

50000

beowulf0

run1

Problema:


1641653455Sequential625216905

164165345562521690750000241.8257904

run2

Problema:


1641653455Sequential625216905

164165345562521690750000241.2855225

beowulf5

run1

Problema:


1641653455Sequential625216905

164165345562521690750000236.5175629

run2

Problema:


1641653455Sequential625216905

164165345562521690750000236.1403961

beowulf8

run1

Problema:


1641653455Sequential625216905

164165345562521690750000801.116272

run2

Problema:


1641653455Sequential625216905

164165345562521690750000805.5685425

beowulf16

run1

Problema:


1641653455Sequential625216905

164165345562521690750000117.050354

run2

Problema:


1641653455Sequential625216905

164165345562521690750000118.3657761

607

100000

beowulf0

run1

Problema:


6569912055Sequential2505118086

656991205525051180881000001384.396118

run2

Problema:


6569912055Sequential2505118086

656991205525051180881000001387.828979

beowulf5

run1

Problema:


6569912055Sequential2505118086

656991205525051180881000001269.646729

run2

Problema:


6569912055Sequential2505118086

656991205525051180881000001270.676392

beowulf8

run1

Problema:


6569912055Sequential2505118086

656991205525051180881000003316.035645

run2

Problema:


6569912055Sequential2505118086

656991205525051180881000003296.381348

beowulf16

run1

Problema:


6569912055Sequential2505118086

65699120552505118088100000491.7569275

run2

Problema:


6569912055Sequential2505118086

65699120552505118088100000504.0476074

709

50000

beowulf0

run1

Problema:


1643145388Sequential623786837

164314538862378683950000337.1434326

run2

Problema:


1643145388Sequential623786837

164314538862378683950000337.1317749

beowulf5

run1

Problema:


1643145388Sequential623786837

164314538862378683950000332.9222412

run2

Problema:


1643145388Sequential623786837

164314538862378683950000329.8166809

beowulf8

run1

Problema:


1643145388Sequential623786837

1643145388623786839500001129.134155

run2

Problema:


1643145388Sequential623786837

1643145388623786839500001136.878052

beowulf16

run1

Problema:


1643145388Sequential623786837

164314538862378683950000165.2099915

run2

Problema:


1643145388Sequential623786837

164314538862378683950000164.4545288

709

100000

beowulf0

run1

Problema:


6553347953Sequential2501446153

655334795325014461541000003220.858154

run2

Problema:


6553347953Sequential2501446153

655334795325014461541000003218.05835

beowulf5

run1

Problema:


6553347953Sequential2501446153

655334795325014461541000003260.966064

run2

Problema:


6553347953Sequential2501446153

655334795325014461541000003263.137939

beowulf8

run1

Problema:


6553347953Sequential2501446153

655334795325014461541000007526.094727

run2

Problema:


6553347953Sequential2501446153

655334795325014461541000007687.610352

beowulf16

run1

Problema:


6553347953Sequential2501446153

655334795325014461541000001126.287842

run2

Problema:


6553347953Sequential2501446153

655334795325014461541000001348.139526

809

50000

beowulf0

run1

Problema:


1640204504Sequential624972454

164020450462497245550000188.7664185

run2

Problema:


1640204504Sequential624972454

164020450462497245550000188.4552155

beowulf5

run1

Problema:


1640204504Sequential624972454

164020450462497245550000185.1395874

run2

Problema:


1640204504Sequential624972454

164020450462497245550000185.0117645

beowulf8

run1

Problema:


1640204504Sequential624972454

164020450462497245550000634.4938965

run2

Problema:


1640204504Sequential624972454

164020450462497245550000630.4830322

beowulf16

run1

Problema:


1640204504Sequential624972454

16402045046249724555000091.59538269

run2

Problema:


1640204504Sequential624972454

16402045046249724555000091.65031433

809

100000

beowulf0

run1

Problema:


6564250986Sequential2504513367

656425098625045133721000002053.576904

run2

Problema:


6564250986Sequential2504513367

656425098625045133721000002054.891846

beowulf5

run1

Problema:


6564250986Sequential2504513367

656425098625045133721000001939.881958

run2

Problema:


6564250986Sequential2504513367

656425098625045133721000001918.79248

beowulf8

run1

Problema:


6564250986Sequential2504513367

656425098625045133721000005011.946777

run2

Problema:


6564250986Sequential2504513367

656425098625045133721000004837.681152

beowulf16

run1

Problema:


6564250986Sequential2504513367

65642509862504513372100000771.5793457

run2

Problema:


6564250986Sequential2504513367

65642509862504513372100000743.9428101

947

50000

beowulf0

run1

Problema:


1645790850Sequential624198382

164579085062419838450000425.0844116

run2

Problema:


1645790850Sequential624198382

164579085062419838450000425.4591064

beowulf5

run1

Problema:


1645790850Sequential624198382

164579085062419838450000408.0883179

run2

Problema:


1645790850Sequential624198382

164579085062419838450000407.8194275

beowulf8

run1

Problema:


1645790850Sequential624198382

1645790850624198384500001501.571655

run2

Problema:


1645790850Sequential624198382

1645790850624198384500001514.792847

beowulf16

run1

Problema:


1645790850Sequential624198382

164579085062419838450000224.7654114

run2

Problema:


1645790850Sequential624198382

164579085062419838450000220.1774597

947

100000

beowulf0

run1

Problema:


6571517811Sequential2503042370

657151781125030423731000001818.657837

run2

Problema:


6571517811Sequential2503042370

657151781125030423731000001818.823853

beowulf5

run1

Problema:


6571517811Sequential2503042370

657151781125030423731000001666.956909

run2

Problema:


6571517811Sequential2503042370

657151781125030423731000001662.710083

beowulf8

run1

Problema:


6571517811Sequential2503042370

657151781125030423731000004337.479004

run2

Problema:


6571517811Sequential2503042370

657151781125030423731000004304.633301

beowulf16

run1

Problema:


6571517811Sequential2503042370

65715178112503042373100000643.7877197

run2

Problema:


6571517811Sequential2503042370

65715178112503042373100000660.6271973

1009

50000

beowulf0

run1

Problema:


1640077661Sequential623868781

164007766162386878150000335.5855103

run2

Problema:


1640077661Sequential623868781

164007766162386878150000332.5362549

beowulf5

run1

Problema:


1640077661Sequential623868781

164007766162386878150000323.5028687

run2

Problema:


1640077661Sequential623868781

164007766162386878150000323.5307922

beowulf8

run1

Problema:


1640077661Sequential623868781

1640077661623868781500001118.355103

run2

Problema:


1640077661Sequential623868781

1640077661623868781500001115.620239

beowulf16

run1

Problema:


1640077661Sequential623868781

164007766162386878150000166.1370087

run2

Problema:


1640077661Sequential623868781

164007766162386878150000160.9194336

1009

100000

beowulf0

run1

Problema:


6569682646Sequential2503472173

656968264625034721771000001326.023804

run2

Problema:


6569682646Sequential2503472173

656968264625034721771000001323.400146

beowulf5

run1

Problema:


6569682646Sequential2503472173

656968264625034721771000001263.724365

run2

Problema:


6569682646Sequential2503472173

656968264625034721771000001263.974854

beowulf8

run1

Problema:


6569682646Sequential2503472173

656968264625034721771000003235.939941

run2

Problema:

KNP P=89

Beowulf

8950000747.886230589100000608.3323364

800746.7615356800608.5378418

747.32608.44

2411.99401.94419.241.811.861.782476.73459.93485.261.281.321.25

409.292572459.9275818

401.9393311480.7312622

418.8582153479.9944763

419.2424622477.7159119

410.6402893485.2621765

3289.08285.54294.762.592.622.543422.25409.10442.851.441.491.37

288.355957415.1868896

294.7618408409.1001587

285.5361328411.6361389

291.188446442.8543091

285.5576782432.4755249

4240.36237.05244.903.113.153.054397.24388.17411.761.531.571.48

244.896225403.9352722

239.2999725411.7600098

237.0492859390.1138306

238.3262177388.171051

242.2415466392.2444763

89500002850.368164891000001546.311768

5002850.8247075001545.758789

2850.601546.04

21537.021499.251589.751.851.901.7921179.971126.761219.841.311.371.27

1540.5935061219.844482

1541.4302981140.237183

1514.0728761208.664917

1589.7501221126.755371

1499.2525631204.341675

31070.521056.151086.732.662.702.6231039.761012.261064.981.491.531.45

1070.9680181064.982178

1062.6365971055.480591

1086.7266851012.25769

1076.1022951020.051514

1056.148561046.05127

4876.46848.87895.303.253.363.184995.12968.701016.251.551.601.52

872.59869381016.254456

895.29644781002.895691

872.1132202980.2436523

848.8746948968.696228

893.43988041007.50708

5773.50762.89793.923.693.743.595931.90919.31942.881.661.681.64

764.1020508933.7312622

762.8852539942.8787842

793.9178467920.7296753

783.2210693919.3078003

763.3865967942.8717651

6673.22648.17701.294.234.404.066924.26906.54962.681.671.711.61

684.7937622906.5374146

667.3932495920.9639282

664.4778442916.819519

648.1668091962.680542

701.2907104914.322998

7617.16602.66625.904.624.734.557904.36883.65915.731.711.751.69

602.6555786915.7276611

622.9191284883.6473999

625.8980713913.6972046

607.3922729904.8256226

617.6193237873.262207

895000089100000

800-500800-500

1128.63741.42

2615.30593.72644.901.831.901.752573.30529.02625.511.291.401.19

593.7191162616.3682861

594.3902588529.024292

644.8969116537.6398926

638.2175293625.5136108

605.2785645557.9310303

4371.41340.69397.653.043.312.844448.76424.78501.501.651.751.48

377.2372742424.7812805

340.6868591501.4951477

347.2186279444.7687378

397.6471863442.9904785

394.2655945429.7557983

6276.04265.71285.304.094.253.966437.59412.52461.441.691.801.61

279.4191284416.6627197

285.2971497461.4409485

282.1201782412.5248108

265.7080688456.3088074

267.6360168441.0095215

8244.70212.90280.484.615.304.028395.61385.10404.691.871.931.83

280.4764099395.532074

253.293045396.7980347

223.8310547404.6850891

252.9934692385.1011963

212.8969879395.9093628

8950000437.108886789100000230.1702271

1400422.78884891400238.3803101

429.95234.28

2237.44232.91240.361.811.851.792176.13168.09183.951.331.391.27

237.2677612179.1517944

238.2421417168.0917664

232.906601170.8267212

240.3645172178.6315308

238.4428711183.949234

3169.12167.72170.452.542.562.523160.91152.08168.481.461.541.39

170.4525299160.1579742

168.2289886165.6603546

169.0936584158.1922913

170.126297168.4751129

167.7201233152.0816803

4136.76132.23140.743.143.253.054148.17143.32153.451.581.631.53

132.2340851143.9399872

135.8719635151.9837494

137.7497101143.3235779

140.7428436148.1447754

137.1906891153.44841

Spine Fast Ethernet

8950000331.7854004

1800330.8816833

331.33

2187.98185.56190.991.761.791.73

190.5935516

186.0215607

186.7228088

190.994751

185.563446

4108.67108.44109.003.053.063.04

108.7705612

108.5903015

109.0008621

108.4422684

108.5354156

871.5969.0674.624.634.804.44

74.62387085

71.24820709

69.06201172

71.53001404

71.51041412

1351.5349.4854.056.436.706.13

52.40294266

51.61725616

50.12607956

49.47747421

54.04982758

Spine Myrinet

8950000331.7854004

1800330.8816833

331.33

2181.37178.18185.541.831.861.79

182.0614929

179.7945709

185.5447388

178.1772156

181.2948761

4106.00104.44107.693.133.173.08

104.4406433

106.7957153

105.9263229

107.6935883

105.1462021

879.0274.9383.134.194.423.99

83.12772369

80.09178925

74.92771912

79.14767456

77.81520844

1382.1380.8486.074.034.103.85

81.23005676

86.06661224

80.83776093

80.97046661

81.56281281

Resultados KNP P = 89

Beowulf

PrimeNBest SolutionCPrimeNBest SolutionC

8950,0001,639,893,780623,971,63789100,0006,562,332,5642,499,610,869

500500

Seq2850.60Seq1546.04

ProcsAverageMinimunMaximunSpd-AveSpd-MaxSpd-MinDifferenceProcsAverageMinimunMaximunSpd-AveSpd-MaxSpd-MinDifference

21,537.021,499.251,589.751.851.901.7990.5021,179.971,126.761,219.841.311.371.2793.09

31,070.521,056.151,086.732.662.702.6230.5831,039.761,012.261,064.981.491.531.4552.72

4876.46848.87895.303.253.363.1846.424995.12968.701,016.251.551.601.5247.56

5773.50762.89793.923.693.743.5931.035931.90919.31942.881.661.681.6423.57

6673.22648.17701.294.234.404.0653.126924.26906.54962.681.671.711.6156.14

7617.16602.66625.904.624.734.5523.247904.36883.65915.731.711.751.6932.08


8950,0001,639,893,780623,971,63789100,0006,562,332,5642,499,610,869

800800

Seq747.32Seq608.44


2411.99401.94419.241.811.861.7817.302476.73459.93485.261.281.321.2525.33

3289.08285.54294.762.592.622.549.233422.25409.10442.851.441.491.3733.75

4240.36237.05244.903.113.153.057.854397.24388.17411.761.531.571.4823.59


8950,0001,639,893,780623,971,63789100,0006,562,332,5642,499,610,869

800-500800-500

Seq1128.63Seq741.42


2615.30593.72644.901.831.901.7551.182573.30529.02625.511.291.401.1996.49

4371.41340.69397.653.043.312.8456.964448.76424.78501.501.651.751.4876.71

6276.04265.71285.304.094.253.9619.596437.59412.52461.441.691.801.6148.92

8244.70212.90280.484.615.304.0267.588395.61385.10404.691.871.931.8319.58


8950,0001,639,893,780623,971,63789100,0006,562,332,5642,499,610,869

14001400

Seq429.95Seq234.28


2237.44232.91240.361.811.851.797.462176.13168.09183.951.331.391.2715.86

3169.12167.72170.452.542.562.522.733160.91152.08168.481.461.541.3916.39

4136.76132.23140.743.143.253.058.514148.17143.32153.451.581.631.5310.12

Spine Fast Ethernet

PrimeNBest SolutionC

8950,0001,639,893,780623,971,637

1800

Seq331.33

ProcsAverageMinimunMaximunSpd-AveSpd-MaxSpd-MinDifference

2187.98185.56190.991.761.791.735.43

4108.67108.44109.003.053.063.040.56

871.5969.0674.624.634.804.445.56

1351.5349.4854.056.436.706.134.57

Spine Myrinet


8950,0001,639,893,780623,971,637

1800

Seq331.33


2181.37178.18185.541.831.861.797.37

4106.00104.44107.693.133.173.083.25

879.0274.9383.134.194.423.998.20

1382.1380.8486.074.034.103.855.23

&L&D&C&A&R&P

Resultados KNP P = 89

1111

89

107

127

607

Number of Processors

Speedup

Sunfire 6800 (N = 100,000)

KNP P=709

11111

89

107

127

607

log


Speedup

Sunfire 6800 (N = 100,000)

Resultados KNP P =709

11111

&A

Page &P

89

107

127

607

log2(Procs)

KNP Nodos visitados

11111

89

107

127

607

log2(Procs)


Speedup

Sunfire 6800 (N = 100,000)

QuickSort 5.000.000

11111

89

107

127

607

log2(Procs)

Resultados QuickSort 5.000.000

11111

&A

Page &P

#REF!

#REF!

#REF!

#REF!

log

MatMult 512

00

00

00

00

00

00

N=50.000

N=100.000

Nmero de procesadores

Aceleracin

Cluster ULL (P=89) 500Mhz

Resultados MatMult 512

00

00

00

N=50.000

N=100.000


Aceleracin

Cluster ULL (P = 89) 800Mhz

Posible buen comportamiento

N=50.000

N=100.000


Aceleracin

Cluster ULL (P = 89) 800-500Mhz

ULL 500 Mhz

ULL 800 Mhz

ULL 800-500 Mhz

ULL 1400 Mhz

SPINE 1800 Mhz Fast Ethernet

SPINE 1800 Mhz Myrinet


speedup

Knapsack N=50.000

N=50.000

N=100.000


Aceleracin


N=50.000


Aceleracin

SPINE (P = 89) 1800Mhz Fast Ethernet

N=50.000


Aceleracin

SPINE (P = 89) 1800Mhz Myrinet

00

00

00

00

SPINE 1800 Mhz Fast Ethernet



Aceleracin

Mochila N=50.000 SPINE

ULL 500 Mhz

ULL 800 Mhz

ULL 800-500 Mhz

ULL 1400 Mhz


speedup

Knapsack N = 50.000 ULL

Beowulf

70950000332.92224127091000003260.966064

800329.81668098003263.137939

331.373262.05

2171.87169.11174.601.931.961.9021872.491705.272179.031.741.911.50

169.11227421790.926514

170.16540531785.164551

174.59579471705.271851

174.33406071902.052002

171.12605292179.031494

3144.97142.35150.342.292.332.2031470.911380.841515.752.222.362.15

143.11094671497.821777

146.4396211380.835571

142.63975521515.747559

142.34849551496.69458

150.33609011463.456787

4124.88121.01131.032.652.742.5341279.361186.071406.162.552.752.32

124.05832671366.247681

123.88193511201.218872

121.00601961237.124634

124.43372341186.074341

131.02943421406.159302

709500001129.1341557091000007526.094727

5001136.8780525007687.610352

1133.017606.85

2590.61584.49596.901.921.941.9024445.034429.084460.981.711.721.71

587.7899784429.076172

594.007873513654.26172

584.49133313653.98535

596.90130624460.981934

589.874145513654.45996

3481.88473.50489.732.352.392.3133664.853462.763868.872.082.201.97

489.72955323616.976318

482.07522583868.869873

473.5008853830.020264

488.35266113462.755127

475.71966553545.652344

4407.03400.86417.012.782.832.7243210.572903.833685.992.372.622.06

417.01123053203.208252

408.04043582903.826904

405.64224243685.990967

403.623233089.941406

400.85614013169.888916

5368.34354.26393.913.083.202.8852889.482653.003243.192.632.872.35

364.62585452664.402588

368.98199462894.526367

393.91268922992.306396

359.92477422652.995117

354.26342773243.192871

6332.06325.40340.483.413.483.3362761.192446.862995.772.753.112.54

331.73098752618.531738

325.39926152446.857422

329.98330692829.807617

332.7186892995.765137

340.48388672914.98877

7317.16313.69319.273.573.613.5572355.962294.972454.123.233.313.10

313.69378662454.123535

318.51593022294.965576

319.27484132318.804443

322.60687262348.990723

320.82449342218.103271

70950000709100000

800-500800-500

500.284252.29

2260.13245.17294.501.922.041.7022462.662217.192736.781.731.921.55

245.17219542217.1875

252.67143252736.779297

247.22889712282.607178

294.50186162501.605225

261.06838992575.13208

4193.76144.92254.032.583.451.9741741.981462.542302.852.442.911.85

254.02952581656.553345

184.31370542302.854248

144.92149351593.415771

217.44776921462.540894

168.09135441694.527588

6164.40145.91176.193.043.432.8461324.121210.391517.403.213.512.80

176.19418331517.403076

166.39987181323.878906

145.91043091210.390259

172.85827641224.63147

160.62559511344.296631

8174.93127.09226.622.863.942.2181121.78963.561375.863.794.413.09

127.0864258963.5563354

138.80142211074.9021

226.62348941036.166382

162.01670841158.427368

220.10343931375.862793

70950000165.20999157091000001126.287842

1400164.454528814001348.139526

164.831237.21

295.1494.6096.371.731.741.712691.71622.19748.731.791.991.65

94.67058563687.8057861

94.5976181748.732605

95.04615021724.2920532

96.37287903675.550415

95.03154755622.1938477

375.5574.4577.842.182.212.123585.00555.95607.832.112.232.04

77.83777618577.7873535

74.98164368595.0422363

74.44979095588.3903198

75.62605286555.9546509

74.84589386607.8273926

463.4362.1565.732.602.652.514485.90453.43508.672.552.732.43

62.91823578485.8868713

62.41640472453.429718

63.91430283508.6743469

62.15296936497.1108093

65.7294693484.3955078

Spine Fast Ethernet

709100000867.3009644

1800867.6292114

867.47

2503.82464.84561.401.721.871.55

482.4951477

464.8403015

493.8860779

516.4734497

561.4014893

4384.48360.33401.722.262.412.16

391.6777344

401.7233276

360.3330383

369.3500671

399.3083496

8231.77210.77255.503.744.123.40

232.1401215

255.5014038

216.0979462

244.3478851

210.7703857

13160.03149.56175.165.425.804.95

175.1571503

149.5569

154.8296661

160.5673981

Spine Myrinet

709100000867.3009644

1800867.6292114

867.47

2546.79487.32632.311.591.781.37

490.4764099

487.3229065

535.6986694

632.3133545

588.1174316

4359.67344.87388.452.412.522.23

351.6657715

388.4503784

347.6478271

365.7121582

344.8717041

8242.60221.52256.973.583.923.38

245.1198578

256.9691772

221.5249786

255.4715424

233.9134827

13179.59170.11187.834.835.104.62

170.1144409

187.8299561

184.5726166

183.3001099

172.1497803

Beowulf


70950,0001,643,145,388623,786,837709100,0006,553,347,9532,501,446,153

500500

Seq1133.01Seq7606.85


2590.61584.49596.901.921.941.9012.4124,445.034,429.084,460.981.711.721.7131.91

3481.88473.50489.732.352.392.3116.2333,664.853,462.763,868.872.082.201.97406.11

4407.03400.86417.012.782.832.7216.1643,210.572,903.833,685.992.372.622.06782.16

5368.34354.26393.913.083.202.8839.6552,889.482,653.003,243.192.632.872.35590.20

6332.06325.40340.483.413.483.3315.0862,761.192,446.862,995.772.753.112.54548.91

7317.16313.69319.273.573.613.555.5872,355.962,294.972,454.123.233.313.10159.16


70950,0001,643,145,388623,786,837709100,0006,553,347,9532,501,446,153

800800

Seq331.37Seq3262.05


2171.87169.11174.601.931.961.905.4821,872.491,705.272,179.031.741.911.50473.76

3144.97142.35150.342.292.332.207.9931,470.911,380.841,515.752.222.362.15134.91

4124.88121.01131.032.652.742.5310.0241,279.361,186.071,406.162.552.752.32220.08


70950,0001,643,145,388623,786,837709100,0006,553,347,9532,501,446,153

800-500800-500

Seq500.28Seq4252.29


2260.13245.17294.501.922.041.7049.3322,462.662,217.192,736.781.731.921.55519.59

4193.76144.92254.032.583.451.97109.1141,741.981,462.542,302.852.442.911.85840.31

6164.40145.91176.193.043.432.8430.2861,324.121,210.391,517.403.213.512.80307.01

8174.93127.09226.622.863.942.2199.5481,121.78963.561,375.863.794.413.09412.31


70950,0001,643,145,388623,786,837709100,0006,553,347,9532,501,446,153

14001400

Seq164.83Seq1237.21


295.1494.6096.371.731.741.711.782691.71622.19748.731.791.991.65126.54

375.5574.4577.842.182.212.123.393585.00555.95607.832.112.232.0451.87

463.4362.1565.732.602.652.513.584485.90453.43508.672.552.732.4355.24

Spine Fast Ethernet


709100,0006,553,347,9532,501,446,153

1800

Seq867.47


2503.82464.84561.401.721.871.5596.56

4384.48360.33401.722.262.412.1641.39

8231.77210.77255.503.744.123.4044.73

13160.03149.56175.165.425.804.9525.60

Spine Myrinet


709100,0006,553,347,9532,501,446,153

1800

Seq867.47


2546.79487.32632.311.591.781.37144.99

4359.67344.87388.452.412.522.2343.58

8242.60221.52256.973.583.923.3835.44

13179.59170.11187.834.835.104.6217.72

&L&D&C&A&R&P

0000

89

107

127

607


Speedup

Sunfire 6800 (N = 100,000)

00000

89

107

127

607

log


Speedup

Sunfire 6800 (N = 100,000)

00000

&A

Page &P

89

107

127

607

log2(Procs)

00000

89

107

127

607

log2(Procs)


Speedup

Sunfire 6800 (N = 100,000)

00000

89

107

127

607

log2(Procs)

00000

&A

Page &P

#REF!

#REF!

#REF!

#REF!

log

N=50.000

N=100.000


Aceleracin

Cluster ULL (P=709) 500Mhz

N=50.000

N=100.000


Aceleracin


N=50.000

N=100.000


Aceleracin

Cluster ULL (P = 709) 800-500Mhz

ULL 500 Mhz

ULL 800 Mhz

ULL 800-500 Mhz

ULL 1400 Mhz

SPINE 1800 Mhz FE



Aceleracin

Mochila N=100.000

N=50.000

N=100.000


Aceleracin


N=100.000


Aceleracin

SPINE (P = 709) 1800Mhz Fast Ethernet

N=100.000


Aceleracin

SPINE (P = 709) 1800Mhz Myrinet

ULL 500 Mhz

ULL 800 Mhz

ULL 800-500 Mhz

ULL 1400 Mhz


Aceleracin

Mochila N=100.000 ULL

00

00

00

00

SPINE 1800 Mhz FE



Aceleracin

Mochila N=100.000 SPINE

500 MhzN=50.000P=89

Seq234567

2,614,3921,420,559991,572788,774667,828546,031486,730

Proc.

01,443,947964,844745,645661,634604,854491,135

1,283,4631,059,961891,147730,087619,358561,608

1,365,738911,173846,609758,801571,383576,821

1,339,2551,081,438829,093745,975573,119500,374

1,518,2621,059,507857,844715,932593,389569,672

1,390,1331,015,385834,068722,486592,421539,922

11,406,406950,935806,703725,968574,789508,703

1,571,9171,001,623748,919670,419590,034545,997

1,400,2721,056,073697,564801,267593,183557,636

1,635,637940,979825,154731,894554,779522,524

1,240,688940,135768,976706,890606,617544,292

1,450,984977,949769,463727,288583,880535,830

21,030,280760,134644,912623,192490,362

938,194784,315695,162531,868534,216

1,049,269732,875681,234619,883518,512

940,726727,988679,011592,267498,488

948,437868,164599,963581,390459,565

981,381774,695660,056589,720500,229

3784,270645,849619,829470,162

859,221626,981484,109511,687

816,380630,456588,117463,215

647,611626,239475,466496,208

776,871654,360504,989497,902

776,871636,777534,502487,835

4593,055476,967401,939

569,587505,228451,611

642,886474,233445,678

583,812463,616420,322

573,315540,724423,305

592,531492,154428,571

5477,032414,635

510,856389,355

441,519439,868

473,538446,815

514,597455,232

483,508429,181

6473,391

473,513

514,042

479,116

487,663

485,545

800-500 MhzN=50.000P=89

Seq2468

2,614,3921,357,842793,650565,073416,313

Proc.

020971291358960976757810270

21413521170002991982712161

239663513114851045240700743

24058411433558940904709388

21116281361344894221690370

2,230,5171,327,070969,821724,586

1507830300737194989173643

459406276446216716155999

490480246066229429160233

475560291655217171166450

492555283225190593126188

485,166279,626209,780156,503

21402596974545692876

1275480812833710822

1068034947964698437

1442933877456698993

1200162906583660247

1,277,841903,876692,275

3293570191157175100

262956226421158166

282150215876150435

313068186723159191

298582199201138792

290,065203,876156,337

4913268719599

936523612752

870202656802

795911620234

928962569572

888,973635,792

5207749170763

223038149590

242524157374

192830184702

204431146721

214,114161,830

6690206

665555

615873

634429

633566

647,926

7177198

144860

150887

157535

145809

155,258


Nmero de nodos

Nodos medios computados (500 Mhz)


Nmero de nodos

Nodos computados (500 Mhz)

0

0

0

0

0


Nmero de nodos

Nodos medios computados (800-500 Mhz)

00000000

00000000

00000000

00000000


Nmero de nodos

Nodos computados (800-500 Mhz)

BeowulfRecursiveIterative

2500000079.4359741269.87485504

80081.6916351367.76977539

68.82

220.7920.6720.963.313.333.28

20.81490326

20.74904823

20.96067238

20.66607285

20.76191521

314.5213.5616.004.745.074.30

16.00052834

13.56223774

13.82237816

14.28215599

14.91469193

414.2913.2615.634.825.194.40

13.26381779

14.31311703

14.83181858

13.42148113

15.62960243

2500000048.0230865544.76244736

50047.3779258745.34526062

45.05

223.4323.1223.941.921.951.88

23.94370461

23.1681633

23.56837273

23.36433029

23.12120438

322.8822.5423.971.972.001.88

22.58790779

22.6835537

22.54350471

22.60605621

23.97011757

425.3321.9128.821.782.061.56

21.91417313

23.18014336

24.45664787

28.82420731

28.29302025

521.9619.9025.072.052.261.80

21.38262367

23.38585281

25.07286072

20.07789993

19.90099907

622.4920.2623.582.002.221.91

23.01029205

23.04133415

20.25942993

22.56987381

23.5832634

721.8120.8022.392.072.172.01

20.79640961

22.39462852

22.22525978

23.62381363

23.0675354

25000000

800-500

77.33

229.5528.9930.762.622.672.51

30.75984001

29.48328209

28.99179077

29.13553238

29.4000473

417.7516.4119.004.364.714.07

16.4135704

18.46767616

18.1777153

18.99939156

16.71435738

616.2715.0018.094.755.164.28

16.02812576

18.08687592

14.99854946

15.96458912

16.24725723

815.2312.9317.185.085.984.50

14.26074505

16.44642639

17.17788887

12.93121529

15.325634

250000004.2671289444.458144188

14004.2786917694.46160078

4.46

23.613.603.621.241.241.23

3.615757942

3.613835096

3.605489969

3.604753017

3.605061054

34.153.784.291.081.181.04

4.291343212

4.262543201

4.209438801

3.782787085

4.192961216

44.514.224.740.991.060.94

4.74324894

4.676225185

4.295331001

4.218391895

4.617800236

Spine Fast Ethernet

250000003.7125830653.756660938

18003.7090508943.752368927

3.75

26.256.116.310.600.610.60

6.282154083

6.111098766

6.30720377

6.300533772

6.270221233

410.278.2611.480.370.450.33

11.42951965

11.47532845

10.83744907

9.35370636

8.258748055

810.119.5610.550.370.390.36

9.561342239

10.08680725

10.20119762

10.1518259

10.54567146

138.737.5010.230.430.500.37

7.499276161

10.2289257

9.037597656

8.397551537

8.49518013

Beowulf

PrimeN

25,000,000

500

Seq45.05


223.4323.1223.941.921.951.880.82

322.8822.5423.971.972.001.881.43

425.3321.9128.821.782.061.566.91

521.9619.9025.072.052.261.805.17

622.4920.2623.582.002.221.913.32

721.8120.8022.392.072.172.011.60

PrimeN

25,000,000

800

Seq68.82


220.7920.6720.963.313.333.280.29

314.5213.5616.004.745.074.302.44

414.2913.2615.634.825.194.402.37

PrimeN

25,000,000

800-500

Seq77.33


229.5528.9930.762.622.672.511.77

417.7516.4119.004.364.714.072.59

616.2715.0018.094.755.164.283.09

815.2312.9317.185.085.984.504.25

PrimeN

25,000,000

1400

Seq4.46


23.613.603.621.241.241.230.01

34.153.784.291.081.181.040.51

44.514.224.740.991.060.940.52

Spine Fast Ethernet

PrimeN

25,000,000

1800

Seq3.75


26.256.116.310.600.610.600.20

410.278.2611.480.370.450.333.22

810.119.5610.550.370.390.360.98

138.737.5010.230.430.500.372.73

&L&D&C&A&R&P

1111

89

107

127

607


Speedup

Sunfire 6800 (N = 100,000)

11111

89

107

127

607

log


Speedup

Sunfire 6800 (N = 100,000)

11111

&A

Page &P

89

107

127

607

log2(Procs)

11111

89

107

127

607

log2(Procs)


Speedup

Sunfire 6800 (N = 100,000)

11111

89

107

127

607

log2(Procs)

11111

&A

Page &P

#REF!

#REF!

#REF!

#REF!

log

0

0

0

0

0

0

N=5.000.000


Aceleracin

Cluster ULL 500Mhz

0

0

0

N=5.000.000


Aceleracin

Cluster ULL 800Mhz

0

0

0

0

N=5.000.000


Aceleracin

Cluster ULL 800-500Mhz

1.92265419963.31027349562.61646384761.2357711060.5933279823

1.96928949214.74100483934.3553491611.07523426270.3612924671

1.77842019014.81545425674.7541870490.98884152070.3670671254

2.0512546485.07783628670.4249818854

2.0030310382

2.0661756518

ULL 500 Mhz

ULL 800 Mhz

ULL 800-500 Mhz

ULL 1400 Mhz

SPINE 1800 Mhz FE


Aceleracin

QuickSort N=5.000.000

N=5.000.000


Aceleracin

Cluster ULL 1400Mhz

N=5.000.000


Aceleracin

SPINE 1800Mhz Fast Ethernet

BeowulfRecursiveIterative

51255.4240074217.39098549

80064.7230911317.37613487

17.38

210.4810.4510.501.661.661.66

10.48824596

10.48006916

10.45057392

10.49565411

10.49302197

37.187.157.192.422.432.42

7.187336922

7.154805183

7.190048218

7.157034874

7.186809063

45.985.676.152.913.072.83

6.145885944

5.669380188

6.052734852

6.036333084

6.000104904

RecursiveIterative

51249.8433036837.51736832

50053.1624870337.65361786

37.59

221.3821.2121.451.761.771.75

21.21115112

21.45490074

21.33468437

21.4450798

21.43061638

314.8314.6914.932.532.562.52

14.75371361

14.93150711

14.92503643

14.85558319

14.68775177

411.9211.6112.533.153.243.00

12.52764606

11.95148373

11.85524654

11.63264561

11.61279774

510.4410.2310.583.603.673.55

10.50299931

10.58280563

10.53883076

10.35225105

10.23198032

69.279.159.334.054.114.03

9.281858444

9.292833328

9.151416779

9.315644264

9.329179764

78.418.308.494.474.534.43

8.429540634

8.489068031

8.297622681

8.241680145

8.268388748

512

800-500

23.08

213.5113.5013.521.711.711.71

13.50867367

13.51665783

13.51312542

13.49929333

13.50463009

47.857.708.062.943.002.86

7.704693794

8.055457115

7.925611973

7.833773136

7.71668005

65.995.866.093.853.943.79

5.859429836

6.052252769

5.950535774

6.08951807

6.015676975

85.375.195.664.304.454.07

5.281681061

5.373501778

5.664728165

5.349915981

5.185409069

51217.3439483617.7393074

140017.3517780317.76284599

17.75

211.9011.8911.921.491.491.49

11.8948307

11.89482689

11.91731453

11.89473915

11.91619301

38.168.028.302.182.212.14

8.183294296

8.02425766

8.079161644

8.212553024

8.29794693

46.276.196.342.832.872.80

6.301105022

6.239357948

6.340665817

6.190915108

6.30121994

Spine Fast Ethernet

51214.4095830914.90150547

180014.4299259214.86768627

14.88

29.349.349.351.591.591.59

9.340826035

9.35019207

9.343358994

9.340772629

9.341483116

45.155.105.212.892.922.86

5.12613821

5.130856037

5.104866982

5.209394932

5.201962948

83.283.103.404.544.794.38

3.258775949

3.366005898

3.104240894

3.27869606

3.396981955

133.563.243.984.184.603.74

3.239177942

3.984332085

3.643779039

3.567718983

3.363507032

Beowulf

N

512

500

Seq37.59


221.3821.2121.451.761.771.750.24

314.8314.6914.932.532.562.520.24

411.9211.6112.533.153.243.000.91

510.4410.2310.583.603.673.550.35

69.279.159.334.054.114.030.18

78.418.308.494.474.534.430.19

N

512

800

Seq17.38


210.4810.4510.501.661.661.660.05

37.187.157.192.422.432.420.04

45.985.676.152.913.072.830.48

N

512

800-500

Seq23.08


213.5113.5013.521.711.711.710.02

47.857.708.062.943.002.860.35

65.995.866.093.853.943.790.23

85.375.195.664.304.454.070.48

N

512

1400

Seq17.75


211.9011.8911.921.491.491.490.02

38.168.028.302.182.212.140.27

46.276.196.342.832.872.800.15

Spine Fast Ethernet

N

512

1800

Seq14.88


29.349.349.351.591.591.590.01

45.155.105.212.892.922.860.10

83.283.103.404.544.794.380.29

133.563.243.984.184.603.740.75

&L&D&C&A&R&P

0000

89

107

127

607


Speedup

Sunfire 6800 (N = 100,000)

00000

89

107

127

607

log


Speedup

Sunfire 6800 (N = 100,000)

00000

&A

Page &P

89

107

127

607

log2(Procs)

00000

89

107

127

607

log2(Procs)


Speedup

Sunfire 6800 (N = 100,000)

00000

89

107

127

607

log2(Procs)

00000

&A

Page &P

#REF!

#REF!

#REF!

#REF!

log

0

0

0

0

0

0

N=512


Aceleracin

Cluster ULL 500Mhz

0

0

0

N=512


Aceleracin

Cluster ULL 800Mhz

0

0

0

0

N=512


Aceleracin

Cluster ULL 800-500Mhz

00001.543321257

00002.7974298523

00004.3950068701

004.0508307686

0

0

ULL 500 Mhz

ULL 800 Mhz

ULL 800-500 Mhz

ULL 1400 Mhz

SPINE 1800 Mhz FE


Aceleracin

Multiplicacin de matrices N=512

N=512


Aceleracin

Cluster ULL 1400Mhz

N=512


Aceleracin

SPINE 1800Mhz Fast Ethernet

Cursiva -> El comportamiento parece que empeora mucho al aumentar el nmero de procesadores

NPrimos

50000891276077098099471009

1000001276077098099471009

Matrix ProductDefinition:Strassen algorithm:Lets bey

Distributed Divide and Conquer skeleton

Two dimensional cutting stock Problem: User InterfaceIn this problem we are given a large stock rectangle S of dimension LxW and n types of smaller rectangles (pieces) where the i-th type has dimension lixwi. Furthermore, each problem is now to cut off from the large rectangle a set of small rectangles such that:All pieces have a fixed orientation, i.e., a piece of length l and width w is different from a piece of length w and width l (lw)All applied cuts are of guillotine type, i.e., cut that start form one edge and run parallel to the other two edges.There are at most bi rectangles of type i in the cutting plane, the demand constrain of the i-th piece.The overall profit obtained by i=1ncixi where xi denotes the number of rectangles of type i in the cutting patter, is maximized.

Performance: CALL & LLACMPI PVMStandard LibrariesParallel ArchitecturesWe need a well accepted Parallel Computing Model

BSPLogP

......

_964874463.doc

Communication Network

Memoria

Processor

Memoria

Processor

Memoria

Processor

...

_964881993.doc

Communication Network

Memory

Processor

Memory

Processor

Memory

Processor

...

CALL & LLAC Architecture

Performance: CALL & LLAC#pragma cll mp mp[0] + mp[1]*N + mp[2]*N*N + mp[3]*N*N*N for (i = 0; i < N; i++) { for (j = 0; j < N; j++) { sum = 0; for (k = 0; k < N; k++) sum += A(i,k) * B(k,j); C(i,j) = sum; } }#pragma cll end mpSquare Matrix Product.A, B y C of dimension NN,

Measuring and Predicting Performancewhile(!bqueue.empty()) { auxSp = bqueue.remove(); // pop a problem from the local queue high = auxSp.upper_bound(pbm,auxSol); // upper bound if ( high > bestSol ) { low = auxSp.lower_bound(pbm,auxSol); // lower bound if ( low > bestSol ) { bestSol = low; sol = auxSol; outputPacket.send(MASTER, SOLVE_TAG, bestSol, sol); } if ( high != low ) { // calculate the number of required slaves rSlaves = bqueue.getNumberOfNodes(); op.send(MASTER, BnB_TAG, high, rSlaves); inputPacket.recv(MASTER, nfSlaves, bestSol, rank {1,..., nfSlaves}); if ( nfSlaves >= 0) { auxSp.branch(pbm,bqueue); // branch and save in the local queue for i=0, nfSlaves{ // send subproblems to the assigned slaves auxSp = bqueue.remove();

outputPacket.send(rank, PBM_TAG, auxSp, bestSol, sol); } } // if nfSlaves == DONE the problem is bounded (cut) } }#pragma cll code numvis++; #pragma cll code numvis++;

How to compile?callcckpr. . . . . .

Number of visited Nodes Study

Measuring and Predicting Performanceint main(int argc, char ** argv) { number sol; readKnap(data);

/* obj. sig., capacidad rest., beneficio */ sol = knap( 0, M, 0);

printf("\nsol = ", sol);

return 0;}#pragma cll code double numvis = 0.0;#pragma cll report all

Symbolic Regression ProblemFind the unknown complexity formula starting from the experimental data gathered by CALL.We can use Symbolic Regression: the induction of mathematical expressions on data. Rather than searching for the values of the regression constants, The object of search is a symbolic description of the system.See Scientific Discovery using Genetic Programming by Maarten Keijzer. 2001http://www.cs.vu.nl/mkeijzer/publications/thesis/.Currently we use a fitness function that measures the error of the predictions on the asymptotic side using linear regression on a small sub-sample

Prediction of the RNA Secondary Structure ProblemRNA molecule: string of n characters: R=r1 r2 ... rn such that ri {A, C, G, U}Nucleotides join to free energy:A UG UC GThe iteration space is n x n triangularDependences nonuniform: dependences among non-consecutive stages

TRACER::ULL 2003 ResultsJournals:Authors: Dorta, Len, RodrguezTitle: Comparing MPI and openMP Implementations of the 0-1 Knapsack Problem Journal: Parallel and Distributed Computing Practices. ISSN 1097-2803 (Accepted)Date: 2003Authors: Blanco V., Garca L., Gonzlez J.A., Rodrguez C., Rodrguez G.Title: A Performance Model for the Analysis of OpenMP ProgramsJournal: Parallel and Distributed Computing Practices. ISSN 1097-2803 (Accepted)Date: 2003

TRACER::ULL 2003 ResultsInternational Conferences:Blanco V., Gonzlez J. A., Len C. , Rodrguez C., Rodrguez G. From Complexity Analysis to Performance Analysis. Euro-Par 2003. International Conference on Parallel and Distributed Computing. Klagenfurt, Austria. 26 - 29 August 2003. Dorta I., Len C., Rodrguez C., Rojas A.Parallel Skeletons for Divide and Conquer and Branch and Bound Techniques. 11th euromicro Conference on Parallel and Network-Based Processing. ISSN 1066-6192. Genova, Italy. 5-7 February, 2003. Dorta I., Len C., Rodrguez C. A comparison between MPI and OpenMP Branch-and-Bound Skeletons. 8th International Workshop on High-Level Parallel Programming Models and Supportive Enviroments. ISBN 0-7695-1880-X. Nice, France.22 April, 2003. Dorta I., Len C., Rodrguez C., Rojas A. Parallel Skeletons. Branch-and-Bound and Divide-and-Conquer Techniques. TAM User Group Meeting 2003. Barcelona, Spain. 16 May, 2003Dorta I., Len C., Rodrguez C., Rojas A. MPI and OpenMP implementations of Branch and Bound Skeletons. ParCo2003. Dresden, Germany. 2-5 Septiembre, 2003. Dorta I., Len C., Rodrguez C. Parallel Branch and Bound Skeletons: Message Passing and Shared Memory Implementtions. 5th International Conference on Parallel Processing and Applied Mathematics. Czestochowa, Poland. 7-10 September, 2003. Garca L., Gonzlez J.A., Gonzlez J.C., Len C., Rodrguez C., Rodrguez G. Complexity Driven Performance Analysis. 10th EuroPVM/MPI 2003. Venice, Italy. Sep 29 - Oct 2, 2003.

TRACER::ULL 2003 ResultsNational Conferences:Dorta I., Len C., Rodrguez C. Rodrguez, G., Rojas A. Complejidad Algortmica: de la Teora a la Prctica. JENUI03 (Jornadas de Enseanza Universitaria de la Informtica). ISBN 84-283-2845-5. Cdiz. 9-11 Julio, 2003Gonzlez J.R., Len, C., Rodrguez C., UnesqueletoparaRamificacinyAcotacinDistribuido. XIV Jornadas De Paralelismo. Legans (Madrid). 15-17 septiembre 2003PFCGonzlez J. R., Esqueletos Paralelos Distribuidos. Paradigmas de Ramificacin y Acotacin y Divide y Vencers. Documento de Trabajo Interno del DEIOC: DT-03-07. Julio 2003.

tracer:ull - 2003 barcelona, october 25th, 2003 tracer.ull.es tic2002-04498-c05-05

Documents