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

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. Key Words: Approximation Algorithms, Design of Algorithms, Disk Dimension, Outerplanar Graphs, Pathwidth, Planar Graphs.

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Faisal N. Abu-Khzam, Michael A. Langston
• Keywords: Algorithms, Approximation Algorithms, Disk Dimension, IPL 2007