Approximating the bandwidth via volume respecting embeddings (extended abstract)
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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. There was not much known though on approximation hardness of this problem, till recently. Karpinski and Wirtgen \cite{KaWi97b} showed that there are no polynomial time approximation algorithms with an absolute error guarantee of $n^{1-\epsilon}$ for any $\epsilon