Approximability Distance in the Space of H-Colourability Problems
2009 (English)In: COMPUTER SCIENCE - THEORY AND APPLICATIONS, ISSN 0302-9743, Vol. 5675, 92-104 p.Article in journal (Refereed) Published
A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. We Study the approximability properties of the Weigh feel Maximum H-Colourable Subgraph problem (MAX H-COL). The instances of this problem are edge-weighted graphs G and the objective is to find a subgraph of G that has maximal total edge weight, under the condition that the subgraph has a homomorphism to H note that for H = K-k this problem is equivalent to MAX k-CUT. To this end, we introduce a metric structure on the space of graphs which allows us to extend previously known approximability results to larger classes of graphs. Specifically, the approximation algorithms for MAX CUT by Goemans and Williamson and MAX k-CUT by Frieze and Jerrum can he used to yield non-trivial approximation results for MAX H-COL For a variety of graphs, we show near-optimality results under the Unique Games Conjecture. We also use our method for comparing the performance of Frieze andamp; Jerrums algorithm with Hastads approximation algorithm for general MAX 2-CSP. This comparison is, in most cases, favourable to Frieze andamp; Jerrum.
Place, publisher, year, edition, pages
2009. Vol. 5675, 92-104 p.
optimisation, approximability, graph homomorphism, graph H-colouring, computational complexity
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-21521DOI: 10.1007/978-3-642-03351-3_11OAI: oai:DiVA.org:liu-21521DiVA: diva2:241470