NDLI: New Approximation Techniques for Some Linear Ordering Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rao, Satish Richa, Andra W.
Copyright Year	2004
Abstract	We describe logarithmic approximation algorithms for the NP-hard graph optimization problems of minimum linear arrangement, minimum containing interval graph, and minimum storage--time product. This improves upon the best previous approximation bounds of Even, Naor, Rao, and Schieber [J. ACM, 47 (2000), pp. 585--616] for these problems by a factor of $\Omega$(log log n). We use the lower bound provided by the volume W of a spreading metric for each of the ordering problems above (as defined by Even et al.) in order to find a solution with cost at most a logarithmic factor times W for these problems. We develop a divide-and-conquer strategy where the cost of a solution to a problem at a recursive level is C plus the cost of a solution to the subproblems at this level, and where the spreading metric volume on the subproblems is less than the original volume by $\Omega$(C log n), ensuring that the resulting solution has cost O(log n) times the original spreading metric volume. We note that this is an existentially tight bound on the relationship between the spreading metric volume and the true optimal values for these problems. For planar graphs, we combine a structural theorem of Klein, Plotkin, and Rao [Proceedings of the 25th ACM Symposium on Theory of Computing, 1993, pp. 682--690] with our new recursion technique to show that the spreading metric cost volumes are within an O(log log n) factor of the cost of an optimal solution for the minimum linear arrangement, and the minimum containing interval graph problems.
Starting Page	388
Ending Page	404
Page Count	17
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539702413197
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	spreading metrics Analysis of algorithms and problem complexity Approximation algorithms approximation algorithms Analysis of algorithms interval graph completion storage--time product minimum linear arrangement
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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