An Approximation Algorithm for the Bandwidth Problem on Dense Graphs

The bandwidth problem is the problem of numbering the vertices of a given graph G such that the maximum di erence between two numbers of adjacent vertices is minimal The problem is known to be NP complete Pa and there are only few algorithms for rather special cases of the problem HMM Kr Sa Sm In this paper we present a randomized approximation algorithm for the bandwidth problem restricted to dense graphs and a randomized approximation algorithm for the same problem on directed dense graphs Dept of Computer Science University of Bonn Bonn Research partially supported by DFG Grant KA by the ESPRIT BR Grants and EC US Email marek cs bonn edu Dept of Computer Science University of Bonn Bonn Research partially supported by the ESPRIT BR Grants and EC US Email wirtgen cs bonn edu Dept of Computer Science University of Bonn Bonn Visiting from Dept of Computer Science Thornton Hall University of Virginia VA Research partially supported by Volkswagen Stiftung and Packard Foundation Email alexz cs virginia edu