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A branch-and-cut approach to physical mapping with end-probes

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44750

Kececioglou,  John
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45092

Mutzel,  Petra
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Fulltext (public)

1996-1-027
(Any fulltext), 11KB

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Citation

Christof, T., Jünger, M., Kececioglou, J., Mutzel, P., & Reinelt, G.(1996). A branch-and-cut approach to physical mapping with end-probes (MPI-I-1996-1-027). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A03A-5
Abstract
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~\cite{AKWZ94} first considered a maximum-likelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics. We show that by exploiting information about the end-probes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant 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 first 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 effectively screen errors from larger instances, and solve the edited instance to optimality as a Hamming-Distance Traveling Salesman Problem. This suggests a new combined approach to physical map construction.