Bounding the Size of the Median Graph

Authors:
Miquel Ferrer;Ernest Valveny;Francesc Serratosa
Affiliations:
Computer Vision Center, Dep. Ciències de la Computació, Universitat Autònoma de Barcelona, Bellaterra, Spain;Computer Vision Center, Dep. Ciències de la Computació, Universitat Autònoma de Barcelona, Bellaterra, Spain;Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain
Venue:
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part II
Year:
2007

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Abstract

Median graphs have been presented as an useful tool for capturing the essential information of a set of graphs. The computation of the median graph is a complex task. Exact algorithms are, in the worst case, exponential both in the number of graphs and their size. The known bounds for the minimum and maximum number of nodes of the candidate median graphs are in general very coarse and they can be used to achieve only limited improvements in such algorithms. In this paper we present more accurate bounds based on the well-known concepts of maximum common subgraph and minimum common supergraph. These new bounds on the number of nodes can be used to improve the existing algorithms in the computation of the median graph.