## Abstract

We introduce a multivariate approach for solving weighted parameterized problems. By allowing flexible use of parameters, our approach defines a framework for applying the classic bounded search trees technique. In our model, given an instance of size n of a minimization/maximization problem, and a parameter W≥1, we seek a solution of weight at most/at least W. We demonstrate the usefulness of our approach in solving VERTEX COVER, 3-HITTING SET, EDGE DOMINATING SET and MAX INTERNAL OUT-BRANCHING. While the best known algorithms for these problems admit running times of the form c^{W}n^{O(1)}, for some c>1, our framework yields running times of the form c^{s}n^{O(1)}, where s≤W is the minimum size of a solution of weight at most/at least W. If no such solution exists, s=min{W,m}, where m is the maximum size of a solution. In addition, we analyze the parameter t≤s, the minimum size of a solution.

Original language | English |
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Pages (from-to) | 157-189 |

Number of pages | 33 |

Journal | Journal of Computer and System Sciences |

Volume | 89 |

DOIs | |

State | Published - 1 Nov 2017 |

Externally published | Yes |

## Keywords

- 3-Hitting set
- Edge dominating set
- Parameterized algorithm
- Vertex cover
- Weighted graph problem

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics