An exponential time 2approximation 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 2approximation algorithm for the Bandwidth problem that takes worstcase {Omicron}(1.9797{sup n}) = {Omicron}(3{sup 0.6217n}) time and uses polynomial space. This improves both the previous best 2 and 3approximation algorithms of Cygan et al. which have an {Omicron}*(3{sup n}) and {Omicron}*(2{sup n}) worstcase 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 divideandconquer strategy along with dynamic programming to achieve this improved time bound.
 Authors:

 Los Alamos National Laboratory
 PENNSYLVANIA STATE U
 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):
 LAUR0904594; LAUR094594
TRN: US201020%%610
 DOE Contract Number:
 AC5206NA25396
 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 2approximation algorithm for bandwidth. United States: N. p., 2009.
Web.
Kasiviswanathan, Shiva, Furer, Martin, & Gaspers, Serge. An exponential time 2approximation algorithm for bandwidth. United States.
Kasiviswanathan, Shiva, Furer, Martin, and Gaspers, Serge. Thu .
"An exponential time 2approximation algorithm for bandwidth". United States. https://www.osti.gov/servlets/purl/990799.
@article{osti_990799,
title = {An exponential time 2approximation 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 2approximation algorithm for the Bandwidth problem that takes worstcase {Omicron}(1.9797{sup n}) = {Omicron}(3{sup 0.6217n}) time and uses polynomial space. This improves both the previous best 2 and 3approximation algorithms of Cygan et al. which have an {Omicron}*(3{sup n}) and {Omicron}*(2{sup n}) worstcase 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 divideandconquer 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}
}