On Approximation Hardness of the Bandwidth Problem

The 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 minimal. The problem has a long history and a number of applications and is known to be NP -hard, Papadimitriou [Pa 76]. 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\\Gammaffl for any ffl ? 0 unless P = NP . Dept. of Computer Science, University of Bonn, 53117 Bonn, and International Computer Science Institute, Berkeley, California. Research partially supported by DFG Grant KA 673/4-1, by the ESPRIT BR Grants 7097 and EC-US 030, DIMACS, and by the Max-Planck Research Prize. Email: marek@cs.bonn.edu. y Dept. of Computer Science, ...