A Branch-and-Cut Approach to Physical Mapping of Chromosomes by Unique End-Probes

THOMAS CHRISTOF, MICHAEL JÜNGER, JOHN KECECIOGLU, PETRA MUTZEL, GERHARD REINELT
1997 Journal of Computational Biology  
A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 52{76, 1995) rst considered a maximum-likelihood model of the problem that is equivalent to nding an ordering of the probes that minimizes a weighted sum of errors, and developed several e ective heuristics. We show that by
more » ... ing information about the end-probes of clones, this model can be formulated as a weighted Betweenness Problem. This a ords the signi cant advantage of allowing the well-developed tools of integer linear-programming and branch-and-cut algorithms to be brought to bear on physical mapping, enabling us for the rst time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can e ectively screen errors from larger instances, and solve the edited instance to optimality as a Hamming-Distance Traveling Salesman Problem. This suggests a new approach, a Betweenness-Traveling Salesman hybrid, for constructing physical maps.
doi:10.1089/cmb.1997.4.433 pmid:9385538 fatcat:4cnna4aq45gm3mepesygcnmpzm