### Abstract

Given a graph G=(V,E) and a set R ⊆ V ×V of requests, we consider to assign a set of edges to each node in G so that for every request (u, v) in R the union of the edge sets assigned to u and v contains a path from u to v. The Minimum Certificate Dispersal Problem (MCD) is defined as one to find an assignment that minimizes the sum of the cardinality of the edge set assigned to each node. In this paper, we give an advanced investigation about the difficulty of MCD by focusing on the relationship between its (in)approximability and request structures. We first show that MCD with general R has Θ(logn) lower and upper bounds on approximation ratio under the assumption P≠NP, where n is the number of nodes in G. We then assume R forms a clique structure, called Subset-Full, which is a natural setting in the context of the application. Interestingly, under this natural setting, MCD becomes to be 2-approximable, though it has still no polynomial time approximation algorithm whose factor better than 677/676 unless P=NP. Finally, we show that this approximation ratio can be improved to 3/2 for undirected variant of MCD with Subset-Full.

Original language | English |
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Title of host publication | Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings |

Pages | 56-65 |

Number of pages | 10 |

DOIs | |

Publication status | Published - Dec 1 2009 |

Event | 15th Annual International Conference on Computing and Combinatorics, COCOON 2009 - Niagara Falls, NY, United States Duration: Jul 13 2009 → Jul 15 2009 |

### 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 | 5609 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 15th Annual International Conference on Computing and Combinatorics, COCOON 2009 |
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Country | United States |

City | Niagara Falls, NY |

Period | 7/13/09 → 7/15/09 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings*(pp. 56-65). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5609 LNCS). https://doi.org/10.1007/978-3-642-02882-3_7