### 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) |
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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 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Journal of Mathematical Biology*,

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