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

Article

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

Tatsuya Akutsu*  and Takeyuki Tamura

Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan

* Author to whom correspondence should be addressed.

Received: 30 October 2012; in revised form: 27 January 2013 / Accepted: 7 February 2013 / Published: 18 February 2013

(This article belongs to the Special Issue Graph Algorithms)

Download PDF Full-Text [200 KB, uploaded 18 February 2013 08:17 CET]

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

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