### Abstract

The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b. In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797 ^{n}) = O(3 ^{0.6217n}) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have an O*(3 ^{n}) and O*(2 ^{n}) worst-case time bounds, respectively. Our algorithm is based on constructing bucket decompositions of the input graph. A bucket decomposition partitions the vertex set of a graph into ordered sets (called buckets) of (almost) equal sizes such that all edges are either incident on vertices in the same bucket or on vertices in two consecutive buckets. The idea is to find the smallest bucket size for which there exists a bucket decomposition. The algorithm uses a simple divide-and-conquer strategy along with dynamic programming to achieve this improved time bound.

Original language | English (US) |
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Title of host publication | Parameterized and Exact Computation - 4th International Workshop, IWPEC 2009, Revised Selected Papers |

Pages | 173-184 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 24 2009 |

Event | 4th International Workshop on Parameterized and Exact Computation, IWPEC 2009 - Copenhagen, Denmark Duration: Sep 10 2009 → Sep 11 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 | 5917 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th International Workshop on Parameterized and Exact Computation, IWPEC 2009 |
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Country | Denmark |

City | Copenhagen |

Period | 9/10/09 → 9/11/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Parameterized and Exact Computation - 4th International Workshop, IWPEC 2009, Revised Selected Papers*(pp. 173-184). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5917 LNCS). https://doi.org/10.1007/978-3-642-11269-0_14