A combinatorial approach to the design of vaccines

Luis Martínez, Martin Milanič, Leire Legarreta, Paul Medvedev, Iker Malaina, Ildefonso M. de la Fuente

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1327-1358
Number of pages32
JournalJournal of Mathematical Biology
Volume70
Issue number6
DOIs
StatePublished - Mar 19 2015

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Vaccines
Vaccine
system optimization
Combinatorial optimization
Superstring
family problems
vaccines
Strings
Integer programming
Human immunodeficiency virus 1
HIV-1
Cover
Set Cover
Hill Climbing
Target
Integer
Design
Combinatorial Optimization
Integer Programming
Combinatorial Optimization Problem

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

Martínez, L., Milanič, M., Legarreta, L., Medvedev, P., Malaina, I., & de la Fuente, I. M. (2015). A combinatorial approach to the design of vaccines. Journal of Mathematical Biology, 70(6), 1327-1358. https://doi.org/10.1007/s00285-014-0797-4
Martínez, Luis ; Milanič, Martin ; Legarreta, Leire ; Medvedev, Paul ; Malaina, Iker ; de la Fuente, Ildefonso M. / A combinatorial approach to the design of vaccines. In: Journal of Mathematical Biology. 2015 ; Vol. 70, No. 6. pp. 1327-1358.
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Martínez, L, Milanič, M, Legarreta, L, Medvedev, P, Malaina, I & de la Fuente, IM 2015, 'A combinatorial approach to the design of vaccines', Journal of Mathematical Biology, vol. 70, no. 6, pp. 1327-1358. https://doi.org/10.1007/s00285-014-0797-4

A combinatorial approach to the design of vaccines. / Martínez, Luis; Milanič, Martin; Legarreta, Leire; Medvedev, Paul; Malaina, Iker; de la Fuente, Ildefonso M.

In: Journal of Mathematical Biology, Vol. 70, No. 6, 19.03.2015, p. 1327-1358.

Research output: Contribution to journalArticle

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Martínez L, Milanič M, Legarreta L, Medvedev P, Malaina I, de la Fuente IM. A combinatorial approach to the design of vaccines. Journal of Mathematical Biology. 2015 Mar 19;70(6):1327-1358. https://doi.org/10.1007/s00285-014-0797-4