The Pair Completion algorithm for the Homogeneous Set Sandwich Problem

Authors:
Claudson Bornstein;Celina M. H. de Figueiredo;Vinícius G. P. de Sá
Affiliations:
Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil;Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil;Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil
Venue:
Information Processing Letters
Year:
2006

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Abstract

A homogeneous set is a non-trivial module of a graph, i.e., a non-empty, non-unitary, proper vertex subset such that all its elements present the same outer neighborhood. Given two graphs G"1(V,E"1) and G"2(V,E"2), the Homogeneous Set Sandwich Problem (HSSP) asks whether there exists a graph G"S(V,E"S), E"1@?E"S@?E"2, which has a homogeneous set. This paper presents an algorithm that uses the concept of bias graph [S. Tang, F. Yeh, Y. Wang, An efficient algorithm for solving the homogeneous set sandwich problem, Inform. Process. Lett. 77 (2001) 17-22] to solve the problem in O(nmin{|E"1|,|E@?"2|}logn) time, thus outperforming the other known HSSP deterministic algorithms for inputs where max{|E"1|,|E@?"2|}=@W(nlogn).