The Index-Based Subgraph Matching Algorithm (ISMA): Fast Subgraph Enumeration in Large Networks Using Optimized Search Trees

Sofie Demeyer,Pieter Audenaert,Tom Michoel,Piet Demeester,Mario Pickavet,Jan Fostier,Timothy Ravasi

doi:10.1371/journal.pone.0061183

Abstract

Subgraph matching algorithms are designed to find all instances of predefined subgraphs in a large graph or network and play an important role in the discovery and analysis of so-called network motifs, subgraph patterns which occur more often than expected by chance. We present the index-based subgraph matching algorithm (ISMA), a novel tree-based algorithm. ISMA realizes a speedup compared to existing algorithms by carefully selecting the order in which the nodes of a query subgraph are investigated. In order to achieve this, we developed a number of data structures and maximally exploited symmetry characteristics of the subgraph. We compared ISMA to a naive recursive tree-based algorithm and to a number of well-known subgraph matching algorithms. Our algorithm outperforms the other algorithms, especially on large networks and with large query subgraphs. An implementation of ISMA in Java is freely available at http://sourceforge.net/projects/isma/.

Highlights

Over the last decade, network theory has come to play a central role in our understanding of complex systems in fields as diverse as molecular biology, sociology, economics, the internet, and others [1]
Motivated by problems in biology, where it is necessary to find subgraph instances in graphs with certain characteristics on the links, which define the type of interaction between cellular components [6,22,23], we developed a novel exact subgraph matching algorithm, which uses a search tree to find all instances of a query subgraph in an edge-colored graph without using an additional, usually time consuming, preprocessing step
To demonstrate the strength of the Index-based Subgraph Matching Algorithm (ISMA) algorithm, we compared it to the naive recursive subgraph matching algorithm (RSMA) as well as the algorithm of Ullmann [9], the VF algorithm [10,11] and the VF2 algorithm [12,13], which are state-of-the-art subgraph matching algorithms

Summary

Introduction

Network theory has come to play a central role in our understanding of complex systems in fields as diverse as molecular biology, sociology, economics, the internet, and others [1]. The central question in all these fields is to understand behavior at the level of the whole system from the topology of interactions between its individual constituents. In this respect, the existence of network motifs, small subgraph patterns which occur more often in a network than expected by chance, has turned out to be one of the defining properties of real-world complex networks, in particular biological networks [2]. The difference between the VF and the VF2 algorithm is that the exploration of the search space has been improved in the VF2 algorithm to reduce memory requirements This means that it is faster and can be applied in larger graphs

Methods

Results

Conclusion