NDLI: Nearly linear time approximation schemes for Euclidean TSP and other geometric problems

Content Provider	IEEE Xplore Digital Library
Author	Arora, S.
Copyright Year	1997
Description	Author affiliation: Princeton Univ., NJ, USA (Arora, S.)
Abstract	We present a randomized polynomial time approximation scheme for Euclidean TSP in R/sup 2/ that is substantially more efficient than our earlier scheme (1996) (and the scheme of Mitchell (1996)). For any fixed c>1 and any set of n nodes in the plane, the new scheme finds a (1+1/c)-approximation to the optimum traveling salesman tour in O(n(logn)/sup O(c)/) time. (Our earlier scheme ran in n/sup O(C)/ time.) For points in R/sup d/ the algorithm runs in O(n(logn)/sup (O(/spl radic/dc)/d-1)) time. This time is polynomial (actually nearly linear) for every fixed c, d. Designing such a polynomial-time algorithm was an open problem (our earlier algorithm (1996) ran in superpolynomial time for d/spl ges/3). The algorithm generalizes to the same set of Euclidean problems handled by the previous algorithm, including Steiner Tree, /spl kappa/-TSP, /spl kappa/-MST, etc, although for /spl kappa/-TSP and /spl kappa/-MST the running time gets multiplied by /spl kappa/. We also use our ideas to design nearly-linear time approximation schemes for Euclidean versions of problems that are known to be in P, such as Minimum Spanning Tree and Min Cost Perfect Matching. All our algorithms can be derandomized, though the running time then increases by O(n/sup d/) in R/sup d/. They also have simple parallel implementations (say, in NC/sup 2/).
Starting Page	554
Ending Page	563
File Size	1052554
Page Count	10
File Format	PDF
ISBN	0818681977
ISSN	02725428
DOI	10.1109/SFCS.1997.646145
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1997-10-20
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Algorithm design and analysis Approximation algorithms Cost function Traveling salesman problems Radio access networks Linear programming Engineering profession Libraries Testing
Content Type	Text
Resource Type	Article

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