Physical Mapping with Repeated Probes: The Hypergraph Superstring Problem

We focus on the combinatorial analysis of physical mapping with repeated probes. We present computational complexity results, and we describe and analyze an algorithmic strategy. We are following the research avenue proposed by Karp [9] on modeling the problem as a combinatorial problem – the Hypergraph Superstring Problem – intimately related to the Lander-Waterman stochastic model [16]. We show that a sparse version of the problem is MAXSNP-complete, a result that carries over to the general case. We show that the minimum Sperner decomposition of a set collection, a problem that is related to the Hypergraph Superstring problem, is NP-complete. Finally we show that the Generalized Hypergraph Superstring Problem is also MAXSNP-hard. We present an efficient algorithm for retrieving the PQ-tree of optimal zero repetition solutions, that provides a constant approximation to the optimal solution on sparse data. We provide experimental results on simulated