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2011

Hardness results for approximating the bandwidth

9 years 3 months ago
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 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 Ôlog n/ log log n will imply a quasi-polynomial time algorithm for NP (when c is a sufficiently small constant).
Chandan K. Dubey, Uriel Feige, Walter Unger
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where JCSS
Authors Chandan K. Dubey, Uriel Feige, Walter Unger
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