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Title: An exponential time 2-approximation algorithm for bandwidth

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 {Omicron}(1.9797{sup n}) = {Omicron}(3{sup 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 {Omicron}*(3{sup n}) and {Omicron}*(2{sup 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.

Authors:
 [1];  [2];  [3]
  1. Los Alamos National Laboratory
  2. PENNSYLVANIA STATE U
  3. U OF MONTPELLIER, FRANCE
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
990799
Report Number(s):
LA-UR-09-04594; LA-UR-09-4594
TRN: US201020%%610
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Conference
Resource Relation:
Conference: Fourth International Workshop on Parameterized and Exact Computation ; September 10, 2009 ; Copenhagen, Denmark
Country of Publication:
United States
Language:
English
Subject:
97; ALGORITHMS; DYNAMIC PROGRAMMING; POLYNOMIALS

Citation Formats

Kasiviswanathan, Shiva, Furer, Martin, and Gaspers, Serge. An exponential time 2-approximation algorithm for bandwidth. United States: N. p., 2009. Web.
Kasiviswanathan, Shiva, Furer, Martin, & Gaspers, Serge. An exponential time 2-approximation algorithm for bandwidth. United States.
Kasiviswanathan, Shiva, Furer, Martin, and Gaspers, Serge. Thu . "An exponential time 2-approximation algorithm for bandwidth". United States. https://www.osti.gov/servlets/purl/990799.
@article{osti_990799,
title = {An exponential time 2-approximation algorithm for bandwidth},
author = {Kasiviswanathan, Shiva and Furer, Martin and Gaspers, Serge},
abstractNote = {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 {Omicron}(1.9797{sup n}) = {Omicron}(3{sup 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 {Omicron}*(3{sup n}) and {Omicron}*(2{sup 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.},
doi = {},
url = {https://www.osti.gov/biblio/990799}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2009},
month = {1}
}

Conference:
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