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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: The simplified partial digest problem: Approximation and a graph-theoretic model
Author(s): Blazewicz, Jacek
Burke, Edmund
Kasprzak, Marta
Kovalev, Alexandr
Kovalyov, Mikhail Y
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Keywords: Integer programming
Genome mapping
Combinatorial optimization
Approximation algorithms
Issue Date: Jan-2011
Citation: Blazewicz J, Burke E, Kasprzak M, Kovalev A & Kovalyov MY (2011) The simplified partial digest problem: Approximation and a graph-theoretic model, European Journal of Operational Research, 208 (2), pp. 142-152.
Abstract: The goal of the simplified partial digest problem (SPDP) is motivated by the reconstruction of the linear structure of a DNA chain with respect to a given nucleotide pattern, based on the multiset of distances between the adjacent patterns (interpoint distances) and the multiset of distances between each pattern and the two unlabeled endpoints of the DNA chain (end distances). We consider optimization versions of the problem, called SPDP-Min and SPDP-Max. The aim of SPDP-Min (SPDP-Max) is to find a DNA linear structure with the same multiset of end distances and the minimum (maximum) number of incorrect (correct) interpoint distances. Results are presented on the worst-case efficiency of approximation algorithms for these problems. We suggest a graph-theoretic model for SPDP-Min and SPDP-Max, which can be used to reduce the search space for an optimal solution in either of these problems. We also present heuristic polynomial time algorithms based on this model. In computational experiments with randomly generated and real-life input data, our best algorithm delivered an optimal solution in 100% of the instances for a number of restriction sites not greater than 50.
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