Periodically specified problems: An exponential complexity gap between exact and approximate solutions
- Univ. at Albany, NY (United States). Dept. of Computer Science
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.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 42519
- Report Number(s):
- LA-UR-95-20; CONF-9503122-1; ON: DE95009435; CNN: National Science Foundation Grant CCR 89-03319; Grant CCR 89-05296; Grant CCR 90-06393; Grant CCR 9406611; TRN: 95:003537
- Resource Relation:
- Conference: 27. ACM annual symposium on theory of computing (STOC), Livermore, CA (United States), Mar 1995; Other Information: PBD: 28 Nov 1994
- Country of Publication:
- United States
- Language:
- English
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