An Algorithm Portfolio for the Sub-graph Isomorphism Problem

Abstract

Abstract. This work presents an algorithm for the sub-graph isomorphism problem based on a new pruning technique for directed graphs. During the tree search, the method checks if a new association between two vertices is compatible by considering the structure of their local neighborhoods, represented as the number of limited-length paths of different type originating from each vertex. In addition, randomized versions of the algorithms are studied experimentally by deriving their runtime distributions. Finally, algorithm portfolios consisting of multiple instances of the same randomized algorithm are proposed and analyzed. The experimental results on benchmark graphs demonstrate that the new pruning method is competitive w.r.t. recently proposed techniques. Significantly better results are obtained on sparse graphs. Furthermore, even better results are obtained by the portfolios, when both the average and standard deviation of solution times are considered.

Portfolios of Subgraph Isomorphism Algorithms

“…-by Battiti and Mascia [2], to remove candidate pairs (u, v) ∈ N p × N t such that the number of paths starting from pattern node u is greater than the number of paths starting from target node v; -by Audemard et al [1] to generalise the locally all-different constraint proposed by Solnon [26] so that it ensures that a subset of pattern nodes can be matched with all different compatible target nodes, where compatibility is defined with respect to invariant properties; -by McCreesh and Prosser [15] to filter the set of candidate pairs before starting the search, and to generate additional implied adjacency-like constraints which are processed during search. Audemard et al [1] do not limit the length of paths considered, and iteratively increment the length until no more pairs are removed.…”

“…Audemard et al [1] do not limit the length of paths considered, and iteratively increment the length until no more pairs are removed. Battiti and Mascia [2], and McCreesh and Prosser [15] parameterise their algorithms by the maximum path length considered when counting paths: larger values for this parameter remove more candidate pairs, but are also more time consuming. Battiti and Mascia's experiments show that the best setting depends on the instance considered, and that a portfolio running several randomised versions in time-sharing decreases the total CPU time needed to find a solution for feasible instances.…”

“…Note that Classes 3 and 12 were not considered in the previous experimental study by McCreesh and Prosser [15]. Our set of instances is much larger than that of Battiti and Mascia [2], who were the first to propose algorithm portfolios for subgraph isomorphism problems. Battiti and Mascia only considered a pure parallel portfolio consisting of two randomised solvers without a selection mechanism.…”

An Approach to Graph Matching in the Component of Model Transformations

“…Algorithm of checking the structure of the neighbors for directed hypergraphs [3]. It is an improved backtracking algorithm.…”

“…However they compare this algorithm [3] with the algorithm VF2 (Vento-Foggia 2). While checking algorithm structure neighbors greatly reduced number of analyzed variants, each test takes too much time.…”