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Algorithms 2014, 7(2), 243-252; doi:10.3390/a7020243
Article

Efficient Algorithms for Subgraph Listing

1,*  and 2
1 Department of Computing Science, Umea University, 901 87 Umea, Sweden 2 Department of Computer Science, Lund University, 221 00 Lund, Sweden
* Author to whom correspondence should be addressed.
Received: 6 March 2014 / Revised: 4 May 2014 / Accepted: 7 May 2014 / Published: 15 May 2014
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Abstract

Subgraph isomorphism is a fundamental problem in graph theory. In this paper we focus on listing subgraphs isomorphic to a given pattern graph. First, we look at the algorithm due to Chiba and Nishizeki for listing complete subgraphs of fixed size, and show that it cannot be extended to general subgraphs of fixed size. Then, we consider the algorithm due to Ga̧sieniec et al. for finding multiple witnesses of a Boolean matrix product, and use it to design a new output-sensitive algorithm for listing all triangles in a graph. As a corollary, we obtain an output-sensitive algorithm for listing subgraphs and induced subgraphs isomorphic to an arbitrary fixed pattern graph.
Keywords: subgraph; subgraph isomorphism; subgraph listing; clique; triangle; output-sensitive algorithm; time complexity subgraph; subgraph isomorphism; subgraph listing; clique; triangle; output-sensitive algorithm; time complexity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zechner, N.; Lingas, A. Efficient Algorithms for Subgraph Listing. Algorithms 2014, 7, 243-252.

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