Reconstructing a Hamiltonian Circuit by Querying the Graph: Application to DNA Physical Mapping

Abstract

This paper studies three mathematical models of the multiplex PCR method of genome physical mapping described in [12]. The models are expressed as combinatorial group testing problems of finding an unknown Hamiltonian circuit in the complete graph by means of queries of different type. For each model, an efficient algorithm is proposed that matches asymptotically the information-theoretic lower bound. Keywords: genome physical mapping, combinatorial group testing, algorithms, asymptotic complexity. 1 Introduction 1.1 Biological Motivation This paper studies several mathematical models of the multiplex PCR method of genome physical mapping described in [12]. Physical mapping is the central stage in genome exploration which consists in creating some landmarks or tags throughout the DNA molecule. These landmarks are some specific nucleotide sequences associated with their positions on the molecule. They are usually obtained through the process of cloning which allows to extract some fra..