The Pair Completion algorithm for the Homogeneous Set Sandwich Problem

A homogeneous set is a non-trivial module of a graph, i.e. a nonempty, non-unitary, proper vertex subset such that all its elements present the same outer neighborhood. Given two graphs G1(V, E1), G2(V, E2), the Homogeneous Set Sandwich Problem (HSSP) asks whether there exists a graph GS(V, ES), E1 ES E2, which has a homogeneous set. This paper presents an algorithm that uses the concept of bias graph [13] to solve the HSSP in O(n m log n) time, thus outperforming the other known deterministic algorithms for this problem.

• Type: Journal
• Year: 2006
• Where: IPL
• Authors: Claudson F. Bornstein, Celina M. Herrera de Figueiredo, Vinícius G. P. de Sá
• Keywords: Homogeneous Set Sandwich, IPL 2006, Non-trivial Module, Proper Vertex