Authors: Celina MH de Figueiredo Guilherme D da Fonseca Vinicius GP de Sa Jeremy Spinrad
Publish Date: 2006/05/10
Volume: 46, Issue: 2, Pages: 149-180
Abstract
A homogeneous set is a nontrivial module of a graph ie a nonempty nonunitary proper subset of a graphs vertices such that all its elements present exactly the same outer neighborhood Given two graphs G 1VE 1G 2VE 2 the Homogeneous Set Sandwich Problem HSSP asks whether there exists a sandwich graph G SVE S E 1 subseteq E S subseteq E 2 which has a homogeneous set In 2001 Tang et al published an allfast On2 triangle 2 algorithm which was recently proven wrong so that the HSSPs known upper bound would have been reset thereafter at the former On4 determined by Cerioli et al in 1998 We present notwithstanding new deterministic algorithms which have it established at On3 log m/n We give as well two even faster On3 randomized algorithms whose simplicity might lend them didactic usefulness We believe that besides providing efficient easytoimplement procedures to solve it the study of these new approaches allows a fairly thorough understanding of the problem
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