A note on block-and-bridge preserving maximum common subgraph algorithms for outerplanar graphs

A note on block-and-bridge preserving maximum common subgraph algorithms for outerplanar graphs

Abstract

Schietgat, Ramon and Bruynooghe [18] proposed a polynomial-timealgorithm for computing a maximum common subgraph under the block-and-bridge preserving subgraph isomorphism (BBP-MCS) for outerplanargraphs. We show that the article contains the following errors:(i) The running time of the presented approach is claimed to beO(n2.5)for two graphs of ordern. We show that the algorithm of the au-thors allows no better bound thanO(n4) when using state-of-the-artgeneral purpose methods to solve the matching instances arising assubproblems. This is even true for the special case, where both inputgraphs are trees.(ii) The article suggests that the dissimilarity measure derived fromBBP-MCS is a metric. We show that the triangle inequality is notalways satisfied and, hence, it is not a metric. Therefore, the dissim-ilarity measure should not be used in combination with techniquesthat rely on or exploit the triangle inequality in any way.Where possible, we give hints on techniques that are suitable to improvethe algorithm. [18] L. Schietgat, J. Ramon, and M. Bruynooghe. A polynomial-time maximumcommon subgraph algorithm for outerplanar graphs and its applicationto chemoinformatics.Annals of Mathematics and Artificial Intelligence,69(4):343–376, 2013.doi:10.1007/s10472-013-9335-0.

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Authors
  • Kriege, Nils M.
  • Droschinsky, Andre
  • Mutzel, Petra
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Shortfacts
Category
Journal Paper
Divisions
Data Mining and Machine Learning
Journal or Publication Title
Journal of Graph Algorithms and Applications
ISSN
1526-1719
Page Range
pp. 607-616
Number
4
Volume
22
Date
December 2018
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