A Comparison of Decomposition Methods for the Maximum Common Subgraph Problem

Minot, Maël; Ndiaye, Samba; Solnon, Christine

doi:10.1109/ictai.2015.75

Cited by 5 publications

(7 citation statements)

References 14 publications

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“…Maximum clique algorithms have been extended for thread-parallel search [10,28,44], and in particular, work stealing strategies designed to eliminate exceptionally hard instances by forcing diversity at the top of search [30] could be beneficial in eliminating some of the rare cases where the clique algorithm is many orders of magnitude worse than the CP models. On the CP side, the focus for parallelism has been on decomposition [33], rather than fully dynamic work stealing-it would be interesting to compare these approaches.…”

Section: Resultsmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

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Abstract. The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the subgraph is required to be connected. We introduce a filtering algorithm for this property and show that it may be combined with a restricted branching technique for the constraint-based approach. We show how to implement a similar branching technique in clique-inspired algorithms. Finally, we experimentally compare approaches for the connected version, and see again that the best choice depends on whether graphs have labels.

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Section: Resultsmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

Self Cite

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“…MCS problems are the target of Minot et al [33], who describe a structural decomposition method for constraint programming. Their decomposition generates independent subproblems, which can then be solved in parallel.…”

Section: Parallel Approachesmentioning

confidence: 99%

“…In our pseudo-code this operation is performed with the queue extraction of line 29, but in reality this operation is performed using the CUDA embedded variables representing the block and thread indices. Then, it proceeds through the main cycle of lines [30][31][32][33][34][35][36][37][38], where it follows a pattern similar to the one of function GPUPARALLELMCS. At this level, thread synchronization within the threads belonging to the same block is guaranteed by the SYNCHTHREADS function (mapped on the CUDA __syncthreads instruction).…”

Section: Algorithmmentioning

confidence: 99%

The Maximum Common Subgraph Problem: A Parallel and Multi-Engine Approach

2020

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The maximum common subgraph of two graphs is the largest possible common subgraph, i.e., the common subgraph with as many vertices as possible. Even if this problem is very challenging, as it has been long proven NP-hard, its countless practical applications still motivates searching for exact solutions. This work discusses the possibility to extend an existing, very effective branch-and-bound procedure on parallel multi-core and many-core architectures. We analyze a parallel multi-core implementation that exploits a divide-and-conquer approach based on a thread pool, which does not deteriorate the original algorithmic efficiency and it minimizes data structure repetitions. We also extend the original algorithm to parallel many-core GPU architectures adopting the CUDA programming framework, and we show how to handle the heavily workload-unbalance and the massive data dependency. Then, we suggest new heuristics to reorder the adjacency matrix, to deal with “dead-ends”, and to randomize the search with automatic restarts. These heuristics can achieve significant speed-ups on specific instances, even if they may not be competitive with the original strategy on average. Finally, we propose a portfolio approach, which integrates all the different local search algorithms as component tools; such portfolio, rather than choosing the best tool for a given instance up-front, takes the decision on-line. The proposed approach drastically limits memory bandwidth constraints and avoids other typical portfolio fragility as CPU and GPU versions often show a complementary efficiency and run on separated platforms. Experimental results support the claims and motivate further research to better exploit GPUs in embedded task-intensive and multi-engine parallel applications.

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“…Unfortunately, many of the instances we consider behave more like decision problem instances than optimisation instances: due to the combination of a low solution density, good value-ordering heuristics, and a strong bound function in cases where the optimal solution is relatively large, it is often the case that the runtime is determined almost entirely by how long it takes to find an optimal solution, with the proof of optimality being nearly trivial. Indeed, attempts to parallelise the basic constraint programming approach by static decomposition have had limited success [29].…”

Section: Parallel Searchmentioning

confidence: 99%

Observations from Parallelising Three Maximum Common (Connected) Subgraph Algorithms

Hoffmann

McCreesh

Ndiaye

et al. 2018

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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We discuss our experiences adapting three recent algorithms for maximum common (connected) subgraph problems to exploit multicore parallelism. These algorithms do not easily lend themselves to parallel search, as the search trees are extremely irregular, making balanced work distribution hard, and runtimes are very sensitive to value-ordering heuristic behaviour. Nonetheless, our results show that each algorithm can be parallelised successfully, with the threaded algorithms we create being clearly better than the sequential ones. We then look in more detail at the results, and discuss how speedups should be measured for this kind of algorithm. Because of the difficulty in quantifying an average speedup when so-called anomalous speedups (superlinear and sublinear) are common, we propose a new measure called aggregate speedup.

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A Comparison of Decomposition Methods for the Maximum Common Subgraph Problem

Cited by 5 publications

References 14 publications

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

The Maximum Common Subgraph Problem: A Parallel and Multi-Engine Approach

Observations from Parallelising Three Maximum Common (Connected) Subgraph Algorithms

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