The hardness of approximation: gap location
Computational Complexity
Approximability of maximum splitting of k-sets and some other Apx-complete problems
Information Processing Letters
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Better approximation algorithms for SET SPLITTING and NOT-ALL-EQUAL SAT
Information Processing Letters
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A Tight Characterization of NP with 3 Query PCPs
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Gadgets Approximation, and Linear Programming
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
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We prove hardness results for approximating set splitting problems and also instances of satisfiability problems which have no "mixed" clauses, i.e., every clause has either all its literals unnegated or all of them negated. Results of Håstad [9] imply tight hardness results for set splitting when all sets have size exactly k ≥ 4 elements and also for non-mixed satisfiability problems with exactly k literals in each clause for k ≥ 4. We consider the case k = 3. For the MAX E3-SET SPLITTING problem in which all sets have size exactly 3, we prove an NP-hardness result for approximating within any factor better than 19/20. This result holds even for satisfiable instances of MAX E3-SET SPLITTING, and is based on a PCP construction due to Håstad [9]. For "non mixed Max 3SAT", we give a PCP construction which is a variant of one in [8] and use it to prove the NP-hardness of approximating within a factor better than 11/12, and also a hardness factor of 15/16 + Ɛ (for any Ɛ 0) for the version where each clause has exactly 3 literals (as opposed to up to 3 literals).