Approximating the Minimum Chain Completion problem

Authors:
Tomás Feder;Heikki Mannila;Evimaria Terzi
Affiliations:
268 Waverley Street, Palo Alto, CA 94301, USA;Helsinki Institute of Information Technology, University of Helsinki and Helsinki University of Technology, Finland;IBM ARC, San Jose, CA 95120, USA
Venue:
Information Processing Letters
Year:
2009

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Abstract

A bipartite graph G=(U,V,E) is a chain graph [M. Yannakakis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods 2 (1) (1981) 77-79] if there is a bijection @p:{1,...,|U|}-U such that @C(@p(1))@?@C(@p(2))@?...@?@C(@p(|U|)), where @C is a function that maps a node to its neighbors. We give approximation algorithms for two variants of the Minimum Chain Completion problem, where we are given a bipartite graph G(U,V,E), and the goal is find the minimum set of edges F that need to be added to G such that the bipartite graph G^'=(U,V,E^') (E^'=E@?F) is a chain graph.