An exponential time 2-approximation algorithm for bandwidth

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...

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Bibliographic Details
Published in:Theoretical computer science Vol. 511; pp. 23 - 31
Main Authors: Fürer, Martin, Gaspers, Serge, Kasiviswanathan, Shiva Prasad
Format: Journal Article
Language:English
Published: Elsevier B.V 04.11.2013
Subjects:
Approximation algorithm
Bucket decomposition
Exponential time algorithm
Graph bandwidth
Graph bandwidth
Bucket decomposition
Approximation algorithm
Exponential time algorithm
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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(1.9797n)=O(30.6217n) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have O∗(3n) and O∗(2n) worst-case running 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 to vertices in the same bucket or to 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 divide-and-conquer strategy along with dynamic programming to achieve the improved time bound.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2013.03.024