论文信息 - Faster approximation for maximum independent set on unit disk graph

Faster approximation for maximum independent set on unit disk graph

Abstract Maximum independent set from a given set D of unit disks intersecting a horizontal line can be solved in O ( n 2 ) time and O ( n 2 ) space. As a corollary, we design a factor 2 approximation algorithm for the maximum independent set problem on unit disk graph which takes both time and space of O ( n 2 ) . The best known factor 2 approximation algorithm for this problem runs in O ( n 2 log ⁡ n ) time and takes O ( n 2 ) space [1] , [2] .

[1] Subhash Suri,et al. Label placement by maximum independent set in rectangles , 1998, CCCG.

[2] J. Gross,et al. Graph Theory and Its Applications , 1998 .

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

[4] Wolfgang Maass,et al. Approximation schemes for covering and packing problems in image processing and VLSI , 1985, JACM.

[5] D. W. Wang,et al. A Study on Two Geometric Location Problems , 1988, Information Processing Letters.

[6] F. Roberts. Graph Theory and Its Applications to Problems of Society , 1987 .

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

[8] Gautam K. Das,et al. Improved Algorithm for Maximum Independent Set on Unit Disk Graph , 2016, CALDAM.

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

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

[11] Erik Jan van Leeuwen,et al. Approximation Algorithms for Unit Disk Graphs , 2005, WG.

[12] Ewa Malesinska. Graph-Theoretical Models for Frequency Assignment Problems , 1997 .

[13] Susmita Sur-Kolay,et al. Approximation algorithms for maximum independent set of a unit disk graph , 2015, Inf. Process. Lett..

[14] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .