The Glasgow Subgraph Solver: Using Constraint Programming to Tackle Hard Subgraph Isomorphism Problem Variants

Abstract

The Glasgow Subgraph Solver provides an implementation of state of the art algorithms for subgraph isomorphism problems. It combines constraint programming concepts with a variety of strong but fast domain-specific search and inference techniques, and is suitable for use on a wide range of graphs, including many that are found to be computationally hard by other solvers. It can also be equipped with side constraints, and can easily be adapted to solve other subgraph matching problem variants. We outline its key features from the view of both users and algorithm developers, and discuss future directions.

Finding Subgraphs with Side Constraints

“…Glasgow Subgraph Solver [24] and PathLAD [21] (the two strongest CP-inspired approaches), and to VF2 [10] and RI [6] (simpler algorithms which perform well on easy instances). The high level approach has very slow startup times (which is to be expected as it involves launching a Java virtual machine and reading in a very large table constraint), but much more worryingly, only catches up with the worst other solver in number of instances solved as the timeout approaches.…”

“…This design is based upon the notion that a CP solver and a subgraph solver can have enough of a shared understanding of a problem to solve it co-operatively. Indeed, the Glasgow Subgraph Solver [24] employs a CP approach to solve subgraph-finding problems, but using special data structures and algorithmsfor example, rather than representing the adjacency constraint using an explicit table, it uses bitset adjacency matrices [22]. The solver also exploits various graph invariants involving degrees [36] and paths [2] to further reduce the search space, and employs special search order heuristics [1].…”

“…Finding small "pattern" graphs inside larger "target" graphs is a widely applicable hard problem, with applications including compilers [5], bioinformatics [6,16], chemistry [29], malware detection [8], pattern recognition [17], and the design of mechanical locks [35]. This has led to the development of numerous dedicated algorithms, with the Glasgow Subgraph Solver [24] being the current state of the art [33]. However, practitioners are often interested in versions of the problem with additional restrictions, or side constraints.…”

Solving Graph Homomorphism and Subgraph Isomorphism Problems Faster Through Clique Neighbourhood Constraints

“…Search order heuristics. The solver's default search order heuristics are based upon three principles: that it is good to branch on variables with few remaining values in a domain, that it is good to branch on variables corresponding to high-degree vertices, and that it is good to try mapping to vertices of high degree [McCreesh et al, 2018;Archibald et al, 2019]. These principles do not appear to be specific to subgraph isomorphism, and so we do not alter the search order heuristics.…”

“…However, in application-oriented papers, particularly from bioinformatics and chemistry, the same name is often implicitly used to mean the non-induced version of the problem (which does not require that non-adjacency be preserved) since this more accurately models the real-world problem being solved [Willett, 1999;Ehrlich and Rarey, 2011]. Despite being theoretically hard problems, these applications, along with others in areas including compilers [Blindell et al, 2015], graph databases [McCreesh et al, 2018] and pattern recognition , have given rise to a large amount of research into designing practical algorithms for solving these problems. Most approaches are based either upon very fast but simple backtracking algorithms [Cordella et al, 2004;Bonnici et al, 2013;Carletti et al, 2017] which often but not always perform well on very easy instances, or upon constraint programming algorithms [Zampelli et al, 2010;Solnon, 2010;Audemard et al, 2014;Archibald et al, 2019], which have higher startup costs but that perform vastly better on harder instances and much more consistently on easy instances [McCreesh et al, 2018;Solnon, 2019].…”