
University of Bonn > Department of Computer Science > Chair V  
CSReports 1997  Copyright 1997 University of Bonn, Department of Computer Science, Abt. V  
85178

On Approximation Hardness of the Bandwidth Problem
Marek Karpinski, Juergen Wirtgen [Download PostScript] [Download PDF] The {\em bandwidth problem} is the problem of enumerating the vertices of a given graph $G$ such that the maximum difference between the numbers of adjacent vertices is {\em minimal}. The problem has a long history and a number of applications and is known to be $NP$hard, Papadimitriou \cite{Pap76}. There is not much known though on approximation hardness of this problem. In this paper we show, that there are no efficient polynomial time approximation schemes for the bandwidth problem under some plausible assumptions. Furthermore we show that there are no polynomial time approximation algorithms with an absolute error guarantee of $n^{1\epsilon}$ for any $\epsilon >0$ unless $P=NP$. 

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University of Bonn > Department of Computer Science > Chair V 