### 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 S_{1},…,S_{k} 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 X_{1}, …, X_{n} 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 X_{i} 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 language | English (US) |
---|---|

Pages (from-to) | 1327-1358 |

Number of pages | 32 |

Journal | Journal of Mathematical Biology |

Volume | 70 |

Issue number | 6 |

DOIs | |

State | Published - Mar 19 2015 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Mathematical Biology*,

*70*(6), 1327-1358. https://doi.org/10.1007/s00285-014-0797-4

}

*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.

Research output: Contribution to journal › Article

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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85028248577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028248577&partnerID=8YFLogxK

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 -