Linear-time algorithms for problems on planar graphs with fixed disk dimension

Authors:
Faisal N. Abu-Khzam;Michael A. Langston
Affiliations:
Division of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon;Department of Computer Science, University of Tennessee, Knoxville, TN
Venue:
Information Processing Letters
Year:
2007

Citing 8
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Abstract

The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties of graphs with a given disk dimension are derived, leading to an algorithm to obtain an outerplanar subgraph of a graph with disk dimension k by removing at most 2k - 2 vertices. This reduction is used to obtain linear-time exact and approximation algorithms on graphs with fixed disk dimension. In particular, a linear-time approximation algorithm is presented for the pathwidth problem.