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A variation on the min cut linear arrangement problem

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Abstract

The Min Cut Linear Arrangement problem asks, for a given graphG and a positive integerk, if there exists a linear arrangement ofG's vertices so that any line separating consecutive vertices in the layout cuts at mostk of the edges. A variation of this problem insists that the arrangement be made on a (fixed-degree) tree instead of a line. We show that (1) this problem isNP-complete even whenG is planar; (2) it is easily solved whenG is a tree; and (3) there is a simple characterization for all graphs with cost 2 or less. Our main result is a linear-time algorithm to embed an outerplanar graphG into a spanning tree with cost at most maxdegree(G) + 1. This result is important because it extends to an approximation algorithm for the standard Min Cut Linear Arrangement Problem on outerplanar graphs.

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Authors and Affiliations

  1. EECS Department (M/C 154), University of Illinois at Chicago, Box 4348, 60680, Chicago, IL, USA

    Shai Simonson

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  1. Shai Simonson
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Supported in part by NSF Grant CCR-8710730.

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Simonson, S. A variation on the min cut linear arrangement problem. Math. Systems Theory 20, 235–252 (1987). https://doi.org/10.1007/BF01692067

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  • DOI: https://doi.org/10.1007/BF01692067

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