gergely varró, frederik deckwerth, martin wieber, andy schürr...

Gergely Varró, Frederik Deckwerth, Martin Wieber, Andy Schürr

{gergely.varro,frederik.deckwerth,martin.wieber,andy.schuerr}@es.tu-darmstadt.de

11. April 2023 | Real-Time Systems Lab | Prof. Dr. Andy Schürr | Dr. Gergely Varró | 1

An Algorithm for GeneratingModel-Sensitive Search Plans for EMF Models


Railway Systems and Safety Requirements

Developed in the MOGENTES project [www.mogentes.eu]

ro:Route

d:defines

sp:SwPos sw1:Switch

o1:observes

Model

se1:Sensors1:sensors

sw2:Switch

o2:observes

se2:Sensor

i:inPosition

s2:sensors[2]

[1]

Route

defines

SwPos Switch

observes

Sensorsensors

inPosition

Metamodel

{ordered}

sw1 sw2

sp

ro

se1 se2

Ordered reference navigable in one direction


Ensuring Safety Requirements at Runtime by Pattern Matching

Which sensors, switches and positions must be checked for a route?

ro:Route

d:defines

sp:SwPos sw1:Switch

o1:observes

Model


sw2:Switch

o2:observes

se2:Sensor

i:inPosition

s2:sensors

RO:Route

defines

SWP:SwPos SW:Switch

observes

SE:Sensorsensors

inPosition

Pattern IDX:Integer[2]

[1]

Route

defines

SwPos Switch

observes

Sensorsensors

inPosition

Metamodel

{ordered}

sensors(RO,IDX,SE)

observes(SE,SW)

inPosition(SW,SWP)

defines(RO,SWP)

ConstraintsRO,IDX,SE,SW,SWP

Variables

Non-binary constraint

Pattern matching

sw1 sw2

sp

ro

se1 se2


Motivation

Pattern matcher application scenarios On-the-fly consistency validation

Ensuring safety requirements at runtime Application condition checks in rule-based model transformation tools Bidirectional model synchronization …

Pattern matcher requirements in an industrial context Efficiency Scalability Standard compliance

Goal Improve the runtime performance of pattern matching

Reduce the number of steps Run the pattern matcher on top of EMF models

Search plan: a sequence of operations


Search Plan Driven Pattern Matching I.

ro:Route

d:defines

sp:SwPos sw1:Switch

o1:observes

Model


sw2:Switch

o2:observes

se2:Sensor

i:inPosition

s2:sensors

RO:Route

defines

SWP:SwPos SW:Switch

observes

SE:Sensorsensors

inPosition

Pattern IDX:Integer

roRO

IDX

SE

SW

SWP

B

F

F

F

F

roRO

IDX

SE

SW

spSWP

B

F

F

F

B

roRO

IDX

SE

sw1SW

spSWP

B

F

F

B

B

roRO

1IDX

se1SE

sw1SW

spSWP

B

B

B

B

B

BB

B

F

F

F

F

[2][1]

Adornment: binding information for all variablesOperation: navigation along a defines edge from a Route to a SwPosOperation adornment: binding preconditionRO and SWP must be bound and free, respectively

Free variable SWP get bound by the operation

BFFFF sensors(RO,IDX,SE) BFFBFFBBBFFFB BBBBBBFdefines(RO,SWP) inPosition(SW,SWP) FB

observes(SE,SW)

(Initial) partial match

Variable RO is Bound (mapped) to ro.Variables IDX, SE, SW and SWP are Free (unmapped).

Pattern matcher performs 4 steps (i.e., traverses 4 matches)


Search Plan Driven Pattern Matching II.

ro:Route

d:defines

sp:SwPos sw1:Switch

o1:observes

Model


sw2:Switch

o2:observes

se2:Sensor

i:inPosition

s2:sensors

RO:Route

defines

SWP:SwPos SW:Switch

observes

SE:Sensorsensors

inPosition

Pattern IDX:Integer

roRO

IDX

SE

SW

SWP

B

F

F

F

F

roRO

1IDX

se1SE

SW

spSWP

B

B

B

F

B

roRO

1IDX

se1SE

sw1SW

spSWP

B

B

B

B

B

roRO

2IDX

se2SE

SW

spSWP

B

B

B

F

B

roRO

2IDX

se2SE

sw2SW

spSWP

B

B

B

B

B

roRO

IDX

SE

SW

spSWP

B

F

F

F

B

[2][1]

BFFFF sensors(RO,IDX,SE) BFFBFFBBBFFFB BBBBB

observes(SE,SW) BFBBBFB

BFdefines(RO,SWP) inPosition(SW,SWP) FB

sensors(RO,IDX,SE) BFF

Pattern matcher performs 6 steps with the second search plan.

BacktrackingThe number of pattern matching steps is influenced by the used search plan.

Perform search plan optimization (before pattern matching) to reduce the number of steps(during pattern matching)


Search Plan Optimization Space

Each path (from BFFFF to BBBBB) represents a search plan Which is the best one?

Quantitative characterization needed Weights for operations Costs for partial search plans (i.e., path prefixes) Goal: weights and costs characterize the pattern matching traversal process

Algorithm needed (search plan generation algorithm) Goal: find the best search plan (w.r.t. the cost)

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB

BBBBF inPosition(SW,SWP) BF

BFdefines(RO,SWP)

inPosition(SW,SWP) FB

BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

observes(SE,SW) BF


Search Plan Generation Approaches

Domain-specific (DS) approaches Operation weights and search plan costs

From the metamodel: type and multiplicity information Independent from the model

Always the same search plan for all models Model-sensitive (MS) approaches

Operation weights and search plan costs From model statistics: number of objects/links of a certain type

Different search plans for different models

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)


BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

observes(SE,SW) BF


Model-Sensitive Search Plan Generation Approaches

[1] Giese, Hildebrandt, Seibel: Improved Flexibility and Scalability by Interpreting Story Diagrams

[2] Geiß, Batz, Grund, Hack, Szalkowski: GrGen: A Fast SPO-Based Graph Rewriting Tool

[3] Varró, Varró, Friedl: Adaptive Graph Pattern Matching for Model Transformations Using Model-Sensitive Search Plans

Binary

Cost functionSupported constraints

Model representation

Search plan generation algorithm

GrGen [2]

VIATRA [3]

Fujaba [1]

Simple (product)Own Graph

BinarySimple (sum)Own Graph

Current approach

BinaryN/AEMFBuilt-in greedy

ArbitraryComplex

(pluggable)EMF

(pluggable) Dynamic

programming

4 3 2 1 0


Dynamic Programming Based Search Plan Generation Algorithm

Dynamic programming Table is filled out iteratively

Columns: number of free variables in the initial adornment (+1)

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)

inPosition(SW,SWP)

observes(SE,SW) BF

FB

BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

4 3 2 1 0

BFFFF has 4 free variables

4 3 2 1 0


Algorithmic Problems I.

Exponential number of adornments (25) Store only a limited number of adornments in each column Limit

User-defined parameter of the algorithm (e.g., k=2 in our example) Trade-off between efficiency and optimality Number of rows defined by k

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)

inPosition(SW,SWP)

observes(SE,SW) BF

FB

BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

4 3 2 1 0

1

2


Algorithmic Problems II.

Unnecessary recalculations in case of shared path suffixes Store only the best of those path prefixes that end at the same adornment Adornment check required when inserting into the table

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBB BBBBB


BFdefines(RO,SWP)


BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

4 3 2 1 0

observes(SE,SW) BF

BFFFB

1

2

4 3 2 1 0


Algorithmic Problems III.

Best search plan Sorted columns in increasing order according to the search plan costs Search plan cost comparison required when inserting into the table

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)

inPosition(SW,SWP)

observes(SE,SW) BF

FB

BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

4 3 2 1 0

1

2

4 3 2 1 0


Algorithmic Problems IV.

Adornments without outgoing edges Reachability analysis required when inserting into the table

Not discussed now

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)

inPosition(SW,SWP)

observes(SE,SW) BF

FB

BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

4 3 2 1 0

1

2

4 3 2 1 0


Algorithm Data Structures

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)


BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

observes(SE,SW) BF

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

BFFFF 10

Adornment

Applicable operations

Operation weights(sorted in an increasing order)

Search plancost

Search plan(no operations applied yet)

State


Algorithm Initialization

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)


BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

observes(SE,SW) BF

1

2

4 3 2 1 0

34

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

BFFFF 10

2

1

Initial state goes to the top-left field

34


Algorithm

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

BFFFF 10

1

2

4 3 2 1 0

defines(RO,SWP) BF B***F 1

1 BFFFB 1

2

1 Iterative process On the columns in decreasing order On the rows in increasing order On the present extension operations in weight

increasing order Each iteration creates a new state

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)


BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

observes(SE,SW) BF


Algorithm

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4BFFFF 10

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

1 BFFFB 1

inPosition(SW,SWP) FB ***FB 1

The new state has 3 free variables

3

2

1

BFFFF

observes(SE,SW)


FB

BBBFF

BFFBBBFFFB BBBBB


BFdefines(RO,SWP)


BBBFB

BFBBB




observes(SE,SW) BF

BFdefines(RO,SWP)

observes(SE,SW) BF

2

3

1


Algorithm

4

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

BFFFF 1

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

1 BFFFB 10


sensors(RO,IDX,SE) BFF BFF** 2

2 BBBFF 2

BF B***F 1defines(RO,SWP)

observes(SE,SW) BF **BF* 1

BFFFF

BBBFF

BFFBBBFFFBBFdefines(RO,SWP)


observes(SE,SW) BF

BFdefines(RO,SWP)



2

2

1


Algorithm

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4BFFFF 10

3

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

1 BFFFB 1


2

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BBBFF 2


1

2

1


Algorithm

3

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

1 BFFFB 1

inPosition(SW,SWP) FB ***FB 1 BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BBBFF 2


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BFFBB 1

observes(SE,SW) FB **FB* 1


2 1

Same adornment? NoBetter search

plan?No

0

2

1


Algorithm

1

2

4 3 2 1

2

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BBBFF 2


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BFFBB 1



3

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

1 BFFFB 1


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

3 BBBFB 2



10

2

2

1


Algorithm

1

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BBBFF 2


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BFFBB 1



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

3 BBBFB 2



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4 BBBFB 2

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4 BBBBF 2


inPosition(SW,SWP) BF ***BF 1/2

0

Same adornment? YesBetter search

plan?No No

2

02

1


Algorithm

1

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BBBFF 2


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BFFBB 1



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

3 BBBFB 2



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4 BBBBF 2




3 BFBBB 1



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4 BBBBB 2

observes(SE,SW) BB **BB*


No valid continuation

2

02

1


Algorithm

1

1

2

4 3 2 1 0

BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BBBFF 2


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

2 BFFBB 1



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

3 BBBFB 2



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4 BBBBF 2



BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

4 BBBBB 2

observes(SE,SW) BB **BB*


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

5 BBBBB 2


BF B***F 1

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF BFF** 2

5 BBBBB 2



5 BBBBF 1




6 BBBBF 2



Same adornment?Better search plan?

No

Yes

0

1


Algorithm

1

2

4 3 2 1 0

BF

sensors(RO,IDX,SE)

defines(RO,SWP)

BFF

observes(SE,SW) BB


B***F 1

BFF** 2

4 BBBBB 2

**BB*

***FB 1

Algorithm returns the search plan in T[0][1]


Measurement Results I.

Eager strategy (k=1) suffices in practical cases? Larger k can be better even for small patterns


Measurement Results II.

Search plan cost function makes sense Good correlation between search plan cost and pattern matching steps


Measurement Results III.

Model-sensitive (MS) search plans outperform domain-specific (DS) ones On all test models By nearly 400 steps in average When the pattern has many edges with arbitrary multiplicity


Summary

Pattern matcher Improve runtime performance: reduced number of PM steps Fully implemented Flexible and embeddable into different tools

Model-sensitive search plans Operation weights from the model First such solution for EMF

Search plan generation algorithm General n-ary operations Complex cost functions (not only addition/multiplication) Parameterization: trade-off between efficiency and optimality Usable without the pattern matcher

Complex attribute manipulation in bidirectional transformation

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