On the relation between the common labelling and the median graph

Authors:
Nicola Rebagliati;Albert Solé-Ribalta;Marcello Pelillo;Francesc Serratosa
Affiliations:
Università Ca' Foscari Venezia, Italy;Universitat Rovira i Virgili, Spain;Università Ca' Foscari Venezia, Italy;Universitat Rovira i Virgili, Spain
Venue:
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Year:
2012

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Abstract

In structural pattern recognition, given a set of graphs, the computation of a Generalized Median Graph is a well known problem. Some methods approach the problem by assuming a relation between the Generalized Median Graph and the Common Labelling problem. However, this relation has still not been formally proved. In this paper, we analyse such relation between both problems. The main result proves that the cost of the common labelling upper-bounds the cost of the median with respect to the given set. In addition, we show that the two problems are equivalent in some cases.