Theory of Periodically Specified Problems: Complexity and Approximability
نویسندگان
چکیده
We study the complexity and the efficient approximability of graph and satisfiability problems when specified using various kinds of periodic specifications studied in [Or82a, HT95, Wa93, HW94, Wa93, MH+94]. We obtain two general results. First, we characterize the complexities of several basic generalized CNF satisfiability problems SAT(S) [Sc78], when instances are specified using various kinds of 1and 2-dimensional periodic specifications [Or82a, Wa93, HW94, HW95, CM91, CM93]. We outline how this characterization can be used to prove a number of new hardness results for periodically speciifed problems for various complexity classes. As one corollary, we show that a number of basic NPhard problems become EXPSPACE-hard when inputs are represented using 1-dimensional infinite periodic wide specifications answering an open question in [Or82a]. Second, we outline a simple yet a general technique to devise approximation algorithms with provable worst case performance guarantees for a number of combinatorial problems specified periodically. Our efficient approximation algorithms and schemes are based on extensions of the ideas in [Ba83,HM85,MH+94] and represent the first nontrivial characterization of a class of problems having an -approximation (or PTAS) for periodically specified NEXPTIME-hard problems. Current Address: Los Alamos National Laboratory P.O. Box 1663, MS B265 Los Alamos NM 87545. Email: [email protected]. The work is supported by the Department of Energy under Contract W-7405-ENG-36. Department of Computer Science, University at Albany SUNY, Albany, NY 12222. Email addresses of authors: fhunt,djr,[email protected]. Supported by NSF Grants CCR 90-06396 and CCR94-06611.
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