Randomized on-line algorithms and lower bounds for computing large independent sets in disk graphs

We study the on-line version of the maximum independent set problem, for the case of disk graphs which are graphs resulting from intersections of disks on the plane. In particular, we investigate whether randomization can be used to break known lower bounds for deterministic on-line independent set algorithms and present new upper and lower bounds.

[1]  Johann Hurink,et al.  A Robust PTAS for Maximum Weight Independent Sets in Unit Disk Graphs , 2004, WG.

[2]  Klaus Jansen,et al.  Polynomial-time approximation schemes for geometric graphs , 2001, SODA '01.

[3]  Timothy M. Chan Polynomial-time approximation schemes for packing and piercing fat objects , 2003, J. Algorithms.

[4]  Richard J. Lipton,et al.  Online interval scheduling , 1994, SODA '94.

[5]  W. K. Hale Frequency assignment: Theory and applications , 1980, Proceedings of the IEEE.

[6]  Jan Kratochvíl,et al.  Representing graphs by disks and balls (a survey of recognition-complexity results) , 2001, Discret. Math..

[7]  Amos Fiat,et al.  Competitive non-preemptive call control , 1994, SODA '94.

[8]  Tomomi Matsui,et al.  Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs , 1998, JCDCG.

[9]  Harry B. Hunt,et al.  NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs , 1998, J. Algorithms.

[10]  Charles J. Colbourn,et al.  Unit disk graphs , 1991, Discret. Math..

[11]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[12]  Harry B. Hunt,et al.  Simple heuristics for unit disk graphs , 1995, Networks.

[13]  W. Kern,et al.  A robust PTAS for maximum independent sets in unit disk graphs , 2004 .

[14]  Thomas Erlebach,et al.  Independence and Coloring Problems on Intersection Graphs of Disks , 2006, Efficient Approximation and Online Algorithms.

[15]  Magnús M. Halldórsson,et al.  Approximating discrete collections via local improvements , 1995, SODA '95.

[16]  Dorit S. Hochbaum,et al.  Efficient bounds for the stable set, vertex cover and set packing problems , 1983, Discret. Appl. Math..