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Algorithms 2013, 6(1), 119-135; doi:10.3390/a6010119

A Polynomial-Time Algorithm for Computing the Maximum Common Connected Edge Subgraph of Outerplanar Graphs of Bounded Degree

Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan
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Received: 30 October 2012 / Revised: 27 January 2013 / Accepted: 7 February 2013 / Published: 18 February 2013
(This article belongs to the Special Issue Graph Algorithms)
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Abstract

The maximum common connected edge subgraph problem is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs, where it has applications in pattern recognition and chemistry. This paper presents a dynamic programming algorithm for the problem when the two input graphs are outerplanar graphs of a bounded vertex degree, where it is known that the problem is NP-hard, even for outerplanar graphs of an unbounded degree. Although the algorithm repeatedly modifies input graphs, it is shown that the number of relevant subproblems is polynomially bounded, and thus, the algorithm works in polynomial time.
Keywords: maximum common subgraph; outerplanar graph; dynamic programming maximum common subgraph; outerplanar graph; dynamic programming
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Akutsu, T.; Tamura, T. A Polynomial-Time Algorithm for Computing the Maximum Common Connected Edge Subgraph of Outerplanar Graphs of Bounded Degree. Algorithms 2013, 6, 119-135.

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