The Complexity of the Approximation of the Bandwidth Problem
نویسنده
چکیده
The bandwidth problem has a long history and a number of important applications. It 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. We will show for any constant k 2 IN that there is no polynomial time approximation algorithm with an approximation factor of k. Furthermore, we will show that this result holds also for caterpillars, a class of restricted trees. We construct for any x; " 2 IR with x > 1 and " > 0 a graph class for which an approximation algorithm with an approximation factor of x+ " exists, but the approximation of the bandwidth problem within a factor of x " is NPcomplete. The best previously known approximation factors for the intractability of the bandwidth approximation problem were 1:5 for general graphs and 4=3 for trees.
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