Thesis:On the development of numerical

parallel algorithms for the insetting procedure

Master of Science in Communication & Information Systems

 

Department of Informatics & CommunicationsTEI of Central Macedonia

Christos Christodoulou

Supervisor D.Varsamis Lecturer

Objectives

Find the optimal number of insets

Find insets with numerical Logic

The algorithm can be used not only at maps

Cartography

From Greek χάρτης hartes, "map" and γράφειν graphein, "write") is the study and practice of making maps.

Map construction is one of the oldest human activities.

According to archaeologists older projects have been and could still qualify maps dating to 30,000 years ago

Island Cartography

Deals with special cartographic problems The need of inset map creation for very small islands

sometimes isolated ones

Must be displayed in the main map Key factor for insetting in Island is the “complexity of

land discontinuity”

Example Map Chalkidiki

Existing Method

Algorithm Calculate the Q

correlation Uses standard frames Search step by step all

the map

Example

Step 1

Step 2

Step 3

Numerical Algorithm

Find insets without searching with standard frames Calculate the maximum Q correlation that the

selection area can be maximized Uses only addition of the map pixels

Numerical Algorithm example 1

Example map Rasterized Map

At this example we use a matrix 4 x 8, inset selection 1x1 and q=3.

Numerical Algorithm example 2

Count zeros for each row an increase the row counter

When it finds ones reset the counter until find zero again

Numerical Algorithm example 3

Count the threes for each column an increase the column counter

When it finds different number reset the counter until find three again

Numerical Algorithm example 4

At the final Matrix we just search if it has the q*im = 3

Parallel implementation

Parallel implementation

Implementation Cases

Many ways and execution scenarios SPMD Tasks

Examine two scenarios N ( accuracy ) according to number of workers N (accuracy ) has the maximum value

Case 1 N = Workers

map N Labs Time sec Insets q Inset Dim.

50.tif 8 8 4.442 920 2 50x50

50.tif 16 16 5.506 29 2.297 50x50

50.tif 32 32 7.418 29 2.287 50x50

50.tif 64 64 11.941 29 2.283 50x50

As we can see at the results the time increases as we increase the number of workers instead of reducing. This is happened because we have delay for the communication time.

Workers - Time

Case 2 N stable

map N Labs Time sec Insets q Inset Dim.

50.tif 64 1 20.761 29 2.283 50x50

50.tif 64 4 18.830 29 2.283 50x50

50.tif 64 8 11.369 29 2.283 50x50

50.tif 64 16 8.485 29 2.283 50x50

50.tif 64 32 8.399 29 2.283 50x50

50.tif 64 64 11.359 29 2.283 50x50

Workers-Time ( N stable)

N stable Speed Up - Efficiency

  1-core 4-cores 8-cores 16-cores 32-cores 64-

cores

S 1.0000 1.1025 1.8261 2.4467 2.4718 1.8277

E 1.0000 0.2756 0.2282 0.1529 0.0772 0.1848

Workers-Speed Up ( N stable)

Workers-Efficiency N stable

Conclusion

The theoretical computational time of the numerical parallel algorithm is almost the same with the logical parallel algorithm.

The efficiency of the numerical algorithm is in general very good, helping the cartographers who use the algorithm to reduce its execution time in a local machine with multicore processor or to a grid computer.

Future Work

Use different methods for parallel implementation SMPMD Tasks

Transform the algorithm to a web-based application in parallel architecture distributed memory in a network of computers or in a grid computer