Periodically specified problems: An exponential complexity gap between exact and approximate solutions

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We study both the complexity and approximability of various graph and combinatorial problems specified using two dimensional narrow periodic specifications (see [CM93, HW92, KMW67, KO91, Or84b, Wa93]). The following two general kinds of results are presented. (1) We prove that a number of natural graph and combinatorial problems are NEXPTIME- or EXPSPACE-complete when instances are so specified; (2) In contrast, we prove that the optimization versions of several of these NEXPTIME-, EXPSPACE-complete problems have polynomial time approximation algorithms with constant performance guarantees. Moreover, some of these problems even have polynomial time approximation schemes. We also sketch how our NEXPTIME-hardness results ... continued below

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19 p.

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Hunt, H.B. III; Rosenkrantz, D.J.; Stearns, R.E.; Marathe, M.V. & Radhakrishnan, V. November 28, 1994.

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Description

We study both the complexity and approximability of various graph and combinatorial problems specified using two dimensional narrow periodic specifications (see [CM93, HW92, KMW67, KO91, Or84b, Wa93]). The following two general kinds of results are presented. (1) We prove that a number of natural graph and combinatorial problems are NEXPTIME- or EXPSPACE-complete when instances are so specified; (2) In contrast, we prove that the optimization versions of several of these NEXPTIME-, EXPSPACE-complete problems have polynomial time approximation algorithms with constant performance guarantees. Moreover, some of these problems even have polynomial time approximation schemes. We also sketch how our NEXPTIME-hardness results can be used to prove analogous NEXPTIME-hardness results for problems specified using other kinds of succinct specification languages. Our results provide the first natural problems for which there is a proven exponential (and possibly doubly exponential) gap between the complexities of finding exact and approximate solutions.

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19 p.

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OSTI as DE95009435

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  • 27. ACM annual symposium on theory of computing (STOC), Livermore, CA (United States), Mar 1995

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  • Other: DE95009435
  • Report No.: LA-UR--95-20
  • Report No.: CONF-9503122--1
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 42519
  • Archival Resource Key: ark:/67531/metadc683575

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  • November 28, 1994

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  • July 25, 2015, 2:20 a.m.

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  • Feb. 29, 2016, 6:53 p.m.

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Hunt, H.B. III; Rosenkrantz, D.J.; Stearns, R.E.; Marathe, M.V. & Radhakrishnan, V. Periodically specified problems: An exponential complexity gap between exact and approximate solutions, article, November 28, 1994; New Mexico. (digital.library.unt.edu/ark:/67531/metadc683575/: accessed December 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.