Hardness results for approximating the bandwidth

The bandwidth of an n-vertex graph G is the minimum value b such that the vertices of G can be mapped to distinct integer points on a line without any edge being stretched to a distance more than b. Previous to the work reported here, it was known that it is NP-hard to approximate the bandwidth with...

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Bibliographic Details
Published inJournal of computer and system sciences Vol. 77; no. 1; pp. 62 - 90
Main Authors Dubey, Chandan, Feige, Uriel, Unger, Walter
Format Journal Article
LanguageEnglish
Published Elsevier Inc 2011
Subjects
Algorithms
Approximation
Bandwidth
C (programming language)
Caterpillar
Circular arc graph
Gap amplification
Graphs
Hardness
Mathematical analysis
Circular arc graph
Gap amplification
Caterpillar
Online AccessGet full text
ISSN0022-0000
1090-2724
DOI10.1016/j.jcss.2010.06.006

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Summary:The bandwidth of an n-vertex graph G is the minimum value b such that the vertices of G can be mapped to distinct integer points on a line without any edge being stretched to a distance more than b. Previous to the work reported here, it was known that it is NP-hard to approximate the bandwidth within a factor better than 3/2. We improve over this result in several respects. For certain classes of graphs (such as cycles of cliques) for which it is easy to approximate the bandwidth within a factor of 2, we show that approximating the bandwidth within a ratio better than 2 is NP-hard. For caterpillars (trees in which all vertices of degree larger than two lie on one path) we show that it is NP-hard to approximate the bandwidth within any constant, and that an approximation ratio of c log n / log log n will imply a quasi-polynomial time algorithm for NP (when c is a sufficiently small constant).
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ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2010.06.006