Experimental Evaluation of Subgraph Isomorphism Solvers

International audienceSubgraph 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

A Parallel, Backjumping Subgraph Isomorphism Algorithm Using Supplemental Graphs

This registry entry contains a reference to the code, data and experimental scripts needed to reproduce the subgraph isomorphism paper: Ciaran McCreesh and Patrick Prosser, "A Parallel, Backjumping Subgraph Isomorphism Algorithm using Supplemental Graphs". To appear at the 21st International Conference on Principles and Practice of Constraint Programming (CP 2015)

Sequential and parallel solution-biased search for subgraph algorithms

Funding: This work was supported by the Engineering and Physical Sciences Research Council (grant numbers EP/P026842/1, EP/M508056/1, and EP/N007565).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.Postprin

A biologically inspired network design model

A network design problem is to select a subset of links in a transport network that satisfy passengers or cargo transportation demands while minimizing the overall costs of the transportation. We propose a mathematical model of the foraging behaviour of slime mould P. polycephalum to solve the network design problem and construct optimal transport networks. In our algorithm, a traffic flow between any two cities is estimated using a gravity model. The flow is imitated by the model of the slime mould. The algorithm model converges to a steady state, which represents a solution of the problem. We validate our approach on examples of major transport networks in Mexico and China. By comparing networks developed in our approach with the man-made highways, networks developed by the slime mould, and a cellular automata model inspired by slime mould, we demonstrate the flexibility and efficiency of our approach

SAT-Based Combinational and Sequential Dependency Computation

We present an algorithm for computing both functional dependency and unateness of combinational and sequential Boolean func- tions represented as logic networks. The algorithm uses SAT-based tech- niques from Combinational Equivalence Checking (CEC) and Automatic Test Pattern Generation (ATPG) to compute the dependency matrix of multi-output Boolean functions. Additionally, the classical dependency definitions are extended to sequential functions and a fast approximation is presented to efficiently yield a sequential dependency matrix. Exten- sive experiments show the applicability of the methods and the improved robustness compared to existing approaches

Searching for Maximum Cliques with Ant Colony Optimization

In this paper, we investigate the capabilities of Ant Colony Optimization (ACO) for solving the maximum clique problem. We describe Ant-Clique, an algorithm that successively generates maximal cliques through the repeated addition of vertices into partial cliques