TY - JOUR

T1 - A combinatorial approach to the design of vaccines

AU - Martínez, Luis

AU - Milanič, Martin

AU - Legarreta, Leire

AU - Medvedev, Paul

AU - Malaina, Iker

AU - de la Fuente, Ildefonso M.

N1 - Funding Information:
Luis Martínez and Leire Legarreta were supported by the Spanish Government, grant MTM2011-28229-C02-02, partly with FEDER funds, by the Basque Government, grant IT753-13. Luis Martínez, Leire Legarreta and Ildefonso M. de la Fuente were supported by the University-Society grant US11/13 of the UPV/EHU. Martin Milanič was supported in part by the Slovenian Research Agency (research program P- and research projects J-, J-, J, MU-PROM/- and N-: GReGAS, supported in part by the European Science Foundation). Technical and human support provided by IZO-SGIker (UPV/EHU, MICINN, GV/EJ, ESF) is gratefully acknowledged.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

PY - 2015/3/19

Y1 - 2015/3/19

N2 - We present two new problems of combinatorial optimization and discuss their applications to the computational design of vaccines. In the shortest λ-superstring problem, given a family S1,…,Sk of strings over a finite alphabet, a set T of “target” strings over that alphabet, and an integer λ, the task is to find a string of minimum length containing, for each i, at least λ target strings as substrings of i. In the shortest λ-cover superstring problem X1, …, Xn of finite sets of strings over a finite alphabet and an integer λ, the task is to find a string of minimum length containing, for each i, at least λ elements of Xi as substrings. The two problems are polynomially equivalent, and the shortest λ-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 λ-superstring and λ-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.

AB - We present two new problems of combinatorial optimization and discuss their applications to the computational design of vaccines. In the shortest λ-superstring problem, given a family S1,…,Sk of strings over a finite alphabet, a set T of “target” strings over that alphabet, and an integer λ, the task is to find a string of minimum length containing, for each i, at least λ target strings as substrings of i. In the shortest λ-cover superstring problem X1, …, Xn of finite sets of strings over a finite alphabet and an integer λ, the task is to find a string of minimum length containing, for each i, at least λ elements of Xi as substrings. The two problems are polynomially equivalent, and the shortest λ-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 λ-superstring and λ-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.

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U2 - 10.1007/s00285-014-0797-4

DO - 10.1007/s00285-014-0797-4

M3 - Article

C2 - 24859149

AN - SCOPUS:85028248577

VL - 70

SP - 1327

EP - 1358

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 6

ER -