# Bandwidth and profile minimization

• Manfred Wiegers
• Burkhard Monien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 344)

## Abstract

For a class of bandwidth approximation algorithms (called level algorithms), we show that the ratio of the approximation and the exact bandwidth is Ω(log bw(G)-1(n)). Then we give a general approximation algorithm which tries to improve a given layout. It is based on a reordering of a previously generated layout. To generate initial layouts two further level algorithms are introduced.

To compare such algorithms we define two norms for the quality of bandwidth approximation algorithms. The first is influenced by a bound which is inherently given for all level algorithms. The second is influenced by a lower bound for the bandwidth. We have tested the improvement algorithm on many graphs and it provides substantial better bandwidth approximation than all level algorithms.

The bandwidth improvement algorithm is also used for minimizing the profile of a graph. We give a list of results obtained by our algorithm for 30 examples given by G. C. Everstine. So our algorithms becomes comparable with other algorithms which have used these examples as a test set.

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