## Abstract

Given a bounded integer program with n variables and m constraints each with 2 variables we present an O(mU) time and O(m) space feasibility algorithm for such integer programs (where U is the maximal variable range size). We show that with the same complexity we can find an optimal solution for the positively weighted minimization problem for monotone systems. Using the localratio technique we develop an O(nmU) time and O(m) space 2-approximation algorithm for the positively weighted minimization problem for the general case. We further generalize all results to non linear constraints (called axis-convex constraints) and to non linear (but monotone) weight functions. Our algorithms are not only better in complexity than other known algorithms, but they are also considerably simpler, and contribute to the understanding of these very fundamental problems.

Original language | English |
---|---|

Title of host publication | Algorithms - ESA 1999 - 7th Annual European Symposium, Proceedings |

Editors | Jaroslav Nešetřil |

Publisher | Springer Verlag |

Pages | 116-126 |

Number of pages | 11 |

ISBN (Print) | 3540662510, 9783540662518 |

DOIs | |

State | Published - 1999 |

Externally published | Yes |

Event | 7th Annual European Symposium on Algorithms, ESA 1999 - Prague, Czech Republic Duration: 16 Jul 1999 → 18 Jul 1999 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 1643 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th Annual European Symposium on Algorithms, ESA 1999 |
---|---|

Country/Territory | Czech Republic |

City | Prague |

Period | 16/07/99 → 18/07/99 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1999.

## Keywords

- 2SAT
- Approximation algorithm
- Combinatorial optimization
- Integer programming
- Local ratio technique
- Vertex cover