
University of Bonn > Department of Computer Science > Chair V  
CSReports 1997  Copyright 1997 University of Bonn, Department of Computer Science, Abt. V  
85176

NPHardness of the Bandwidth Problem on Dense Graphs
Marek Karpinski, Juergen Wirtgen [Download PostScript] [Download PDF] The {\em bandwidth problem} is the problem of numbering 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 and varied history and is known to be $NP$hard Papadimitriou \cite{Pap76}. Recently for dense graphs a constant ratio approximation algorithm for this problem has been constructed in Karpinski, Wirtgen and Zelikovsky \cite{KaWiZe97}. In this paper we prove that the bandwidth problem on the dense instances remains $NP$hard. 

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08/18/99 at 13:00:38
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University of Bonn > Department of Computer Science > Chair V 