A subgraph isomorphism algorithm and its application to biochemical data

Abstract

BackgroundGraphs can represent biological networks at the molecular, protein, or species level. An important query is to find all matches of a pattern graph to a target graph. Accomplishing this is inherently difficult (NP-complete) and the efficiency of heuristic algorithms for the problem may depend upon the input graphs. The common aim of existing algorithms is to eliminate unsuccessful mappings as early as and as inexpensively as possible.ResultsWe propose a new subgraph isomorphism algorithm which applies a search strategy to significantly reduce the search space without using any complex pruning rules or domain reduction procedures. We compare our method with the most recent and efficient subgraph isomorphism algorithms (VFlib, LAD, and our C++ implementation of FocusSearch which was originally distributed in Modula2) on synthetic, molecules, and interaction networks data. We show a significant reduction in the running time of our approach compared with these other excellent methods and show that our algorithm scales well as memory demands increase.ConclusionsSubgraph isomorphism algorithms are intensively used by biochemical tools. Our analysis gives a comprehensive comparison of different software approaches to subgraph isomorphism highlighting their weaknesses and strengths. This will help researchers make a rational choice among methods depending on their application. We also distribute an open-source package including our system and our own C++ implementation of FocusSearch together with all the used datasets (http://ferrolab.dmi.unict.it/ri.html). In future work, our findings may be extended to approximate subgraph isomorphism algorithms.

A Comparative Study of Graph Isomorphism Applications

“…Author introduced a subgraph isomorphism algorithm for biochemical data [11]. This algorithm is not using pruning rules and domain reduction procedure which reduces the search space.…”

SuMGra: Querying Multigraphs via Efficient Indexing

“…, f |f | ), and the minimum co-ordinates are the origin of the rectangle (filled with zero values). For example, a data vertex represented by the synopses with two features F v = (2, 3) spans a rectangle in a 2-dimensional space in the interval range ([0, 2], [0,3]). Now if we consider synopses of two query vertices, F u1 = (1, 3) and F u2 = (1, 4), we observe that the rectangle spanned by F u1 is wholly contained in the rectangle spanned by F v but F u2 is not wholly contained in F v .…”

“…We evaluate the performance of SuMGra by comparing it with two baseline approaches (its own variants) and a competitor RI [3]. The two baseline approaches are: (i) SuMGra-No-SC that does not consider the vertex signature index S and it initializes the candidate set of the initial vertex C(u init ) with the whole set of data nodes; (ii) SuMGra-Rand-Order that consider all the indexing structure but it employs a random ordering of the query vertices preserving connectivity.…”

“…Among the vast literature on subgraph isomorphism, [3] is the unique approach, which is a backtracking approach, that is able to directly manage graph with (multiple) labels on the edges. It proposes an approach called RI that uses light pruning rules in order to avoid visiting useless candidates.…”

NetMatchStar: an enhanced Cytoscape network querying app

“…NetMatchStar integrates the RI algorithm proposed for biological real networks which outperforms other existing algorithms 24 . For illustration purposes, NetMatchStar has been tested on a biological dataset 24,32 and an overview of its performance concludes the paper.…”