### Abstract

For a given graph G with positive integral cost and delay on edges, distinct vertices s and t, cost bound C â̂̂ Z ^{+} and delay bound D â̂̂ Z ^{+}, the k bi-constraint path (kBCP) problem is to compute k disjoint st-paths subject to C and D. This problem is known NP-hard, even when k = 1 [4]. This paper first gives a simple approximation algorithm with factor-(2,2), i.e. the algorithm computes a solution with delay and cost bounded by 2 D and 2 C respectively. Later, a novel improved approximation algorithm with ratio is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-(1.369, 2) approximation algorithm by setting and a factor-(1.567, 1.567) algorithm by setting. Besides, by setting β = 0, an approximation algorithm with ratio (1, O(ln n)), i.e. an algorithm with only a single factor ratio O(ln n) on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the kBCP problem that strictly obeys the delay constraint.

Original language | English |
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Title of host publication | Computing and Combinatorics - 19th International Conference, COCOON 2013, Proceedings |

Publisher | Springer Berlin |

Pages | 325-336 |

Number of pages | 12 |

ISBN (Print) | 9783642387678 |

DOIs | |

Publication status | Published - 8 Oct 2013 |

Externally published | Yes |

Event | 19th International Computing and Combinatorics Conference, COCOON 2013 - Hangzhou, China Duration: 21 Jun 2013 → 21 Jun 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7936 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 19th International Computing and Combinatorics Conference, COCOON 2013 |
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Country | China |

City | Hangzhou |

Period | 21/06/13 → 21/06/13 |

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## Cite this

*Computing and Combinatorics - 19th International Conference, COCOON 2013, Proceedings*(pp. 325-336). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7936 LNCS). Springer Berlin. https://doi.org/10.1007/978-3-642-38768-5_30