Observations from Parallelising Three Maximum Common (Connected) Subgraph Algorithms

Hoffmann, R.; McCreesh, Ciaran; Ndiaye, Samba; Prosser, Patrick; Reilly, Craig; Solnon, Christine; Trimble, James

doi:10.1007/978-3-319-93031-2_22

Cited by 3 publications

(9 citation statements)

References 32 publications

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“…Better insights are given by scatter plots that compare times on a per instance basis (as done in Fig. 5), or by the aggregate speed-up measure introduced in [12], which measures timeout ratio for solving a same number of instances. For instance, Sequential Glasgow solves 14, 356 instances within 1000s, and the hardest of these instances is solved in 939s.…”

Section: Combining Solvers To Take the Best Of Themmentioning

confidence: 99%

Experimental Evaluation of Subgraph Isomorphism Solvers

Solnon

2019

Lecture Notes in Computer Science

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Subgraph Isomorphism (SI) is an NP-complete problem which is at the heart of many structural pattern recognition tasks as it involves finding a copy of a pattern graph into a target graph. In the pattern recognition community, the most well-known SI solvers are VF2, VF3, and RI. SI is also widely studied in the constraint programming community, and many constraint-based SI solvers have been proposed since Ullman, such as LAD and Glasgow, for example. All these SI solvers can solve very quickly some large SI instances, that involve graphs with thousands of nodes. However, McCreesh et al. have recently shown how to randomly generate SI instances the hardness of which can be controlled and predicted, and they have built small instances which are computationally challenging for all solvers. They have also shown that some small instances, which are predicted to be easy and are easily solved by constraint-based solvers, appear to be challenging for VF2 and VF3. In this paper, we widen this study by considering a large test suite coming from eight benchmarks. We show that, as expected for an NP-complete problem, the solving time of an instance does not depend on its size, and that some small instances coming from real applications are not solved by any of the considered solvers. We also show that, if RI and VF3 can solve very quickly a large number of easy instances, for which Glasgow or LAD need more time, they fail at solving some other instances that are quickly solved by Glasgow or LAD, and they are clearly outperformed by Glasgow on hard instances. Finally, we show that we can easily combine solvers to take benefit of their complementarity.This work has been done in collaboration with Ciaran McCreesh, Patrick Prosser, and James Trimble. In particular, all experiments have been run by Ciaran McCreesh and used the Cirrus UK National Tier-2 HPC Service at EPCC (http://www.cirrus.ac.uk) funded by the University of Edinburgh and EPSRC (EP/P020267/1).

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Section: Combining Solvers To Take the Best Of Themmentioning

confidence: 99%

Experimental Evaluation of Subgraph Isomorphism Solvers

Solnon

2019

Lecture Notes in Computer Science

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“…vertical distance between two lines therefore shows how many more instances can be solved by one solver than another, if every instance is run separately with the chosen x timeout. The horizontal distance shows how many times longer the per-instance timeout would need to be to allow the rightmost algorithm to succeed on y out of the 14,621 instances (bearing in mind that the two sets of y instances could be different), and gives a measure called aggregate speedup [20].…”

Section: Improving Sequential Searchmentioning

confidence: 99%

“…Exploiting multiple cores to speed up constraint programming solvers remains an active area of research, with no universally perfect solution being available. Four of the more common approaches are based upon decompositions [26,34], work-stealing [39,6,35,20], parallel discrepancy searches [40,41], and algorithm portfolios [32]. Decomposition approaches are unsuitable for decision problems, or problems where we have good value-ordering heuristics, because the decomposition interferes strongly with the shape of the search tree [34].…”

Section: Parallel Searchmentioning

confidence: 99%

“…Decomposition approaches are unsuitable for decision problems, or problems where we have good value-ordering heuristics, because the decomposition interferes strongly with the shape of the search tree [34]. Work-stealing, traditionally, also interferes with value-ordering [36], although specially designed exceptions exist [6,35,20]. However, these have very complicated implementations.…”

Section: Parallel Searchmentioning

confidence: 99%

“…This new form of search can also be parallelised, with a much simpler implementation than conventional work-stealing. By running many threads with different random seeds but the same restart schedule, and sharing nogoods only following restarts, we can achieve aggregate speedups [20] of thirty-one from a thirty-six core machine, or over one hundred by using ten such machines.…”

Section: Introductionmentioning

confidence: 99%

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Sequential and Parallel Solution-Biased Search for Subgraph Algorithms

Archibald

Dunlop

Hoffmann

et al. 2019

Lecture Notes in Computer Science

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The current state of the art in subgraph isomorphism solving involves using degree as a value-ordering heuristic to direct backtracking search. Such a search makes a heavy commitment to the first branching choice, which is often incorrect. To mitigate this, we introduce and evaluate a new approach, which we call "solution-biased search". By combining a slightly-random value-ordering heuristic, rapid restarts, and nogood recording, we design an algorithm which instead uses degree to direct the proportion of search effort spent in different subproblems. This increases performance by two orders of magnitude on satisfiable instances, whilst not affecting performance on unsatisfiable instances. This algorithm can also be parallelised in a very simple but effective way: across both satisfiable and unsatisfiable instances, we get a further speedup of over thirty from thirty-six cores, and over one hundred from ten distributed-memory hosts. Finally, we show that solution-biased search is also suitable for optimisation problems, by using it to improve two maximum common induced subgraph algorithms.

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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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Observations from Parallelising Three Maximum Common (Connected) Subgraph Algorithms

Cited by 3 publications

References 32 publications

Experimental Evaluation of Subgraph Isomorphism Solvers

Experimental Evaluation of Subgraph Isomorphism Solvers

Sequential and Parallel Solution-Biased Search for Subgraph Algorithms

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

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