# Linear time algorithms for k-cutwidth problem

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## Abstract

The Min Cut Linear Arrangement problem is to find a linear arrangement for a given graph such that the cutwidth is minimized. This problem has important applications in VLSI layout systems. It is known that this problem is *NP*-complete when the input is a general graph with maximum vertex degree at most 3. In this paper, we will first present a linear time algorithm to recognize the small cutwidth trees. The approach we used in this algorithm can then be easily extended to recognize the general graphs with cutwidth 3 in O(*n*) time.

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© Springer-Verlag Berlin Heidelberg 1992