Approximation algorithms for the minimum rainbow subgraph problem

Our research was motivated by the pure parsimony haplotyping problem: Given a set G of genotypes, the haplotyping problem consists in finding a set H of haplotypes that explains G. In the pure parsimony haplotyping problem (PPH) we are interested in finding a set H of smallest possible cardinality. The pure parsimony haplotyping problem can be described as a graph colouring problem as follows: The minimum rainbow subgraph problem Given a graph G, whose edges are coloured with p colours. Find a subgraph F ⊆ G of G of minimum order with |E(F )| = p such that each colour occurs exactly once. In this talk we will present polynomial time approximtaion algorithms for the minimum rainbow subgraph problem: • Applying the greedy algorithm we obtain an approximation algorithm with an approximation ratio of ∆(G) for graphs with maximum degree ∆(G). • Based on matching techniques we present an approximation algorithm with an approximation ratio of 5 3 for graphs with maximum degree 2.