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Martinez L.,University of the Basque Country | Martinez L.,Biocruces Health Research Institute Iis Biocruces | Milanic M.,University of Primorska | Legarreta L.,University of the Basque Country | And 7 more authors.
Journal of Mathematical Biology | Year: 2014

We present two new problems of combinatorial optimization and discuss their applications to the computational design of vaccines. In the shortest (Formula presented.)-superstring problem, given a family (Formula presented.) of strings over a finite alphabet, a set (Formula presented.) of "target" strings over that alphabet, and an integer (Formula presented.), the task is to find a string of minimum length containing, for each (Formula presented.), at least (Formula presented.) target strings as substrings of (Formula presented.). In the shortest (Formula presented.)-cover superstring problem, given a collection (Formula presented.) of finite sets of strings over a finite alphabet and an integer (Formula presented.), the task is to find a string of minimum length containing, for each (Formula presented.), at least (Formula presented.) elements of (Formula presented.) as substrings. The two problems are polynomially equivalent, and the shortest (Formula presented.)-cover superstring problem is a common generalization of two well known combinatorial optimization problems, the shortest common superstring problem and the set cover problem. We present two approaches to obtain exact or approximate solutions to the shortest (Formula presented.)-superstring and (Formula presented.)-cover superstring problems: one based on integer programming, and a hill-climbing algorithm. An application is given to the computational design of vaccines and the algorithms are applied to experimental data taken from patients infected by H5N1 and HIV-1. © 2014 Springer-Verlag Berlin Heidelberg.

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