Introduction to algorithms
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Measure, Stochasticity, and the Density of Hard Languages
SIAM Journal on Computing
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Dimension in Complexity Classes
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Theoretical Computer Science
Scaled dimension and nonuniform complexity
Journal of Computer and System Sciences
SIGACT news complexity theory column 48
ACM SIGACT News
The arithmetical complexity of dimension and randomness
ACM Transactions on Computational Logic (TOCL)
Theoretical Computer Science
Scaled dimension and nonuniform complexity
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Online learning and resource-bounded dimension: winnow yields new lower bounds for hard sets
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Hardness hypotheses, derandomization, and circuit complexity
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
| Hi-index | 5.23 |
Under the hypothesis that NP has positive p-dimension, we prove that any approximation algorithm A for MAX3SAT must satisfy at least one of the following: 1. For some δ 0, A uses at least 2nδ time. 2. For all ε 0, A has performance ratio less than 7/8 + ε on an exponentially dense set of satisfiable instances. As a corollary, this solves one of Lutz and Mayordomo's "Twelve problems on resource-bounded measure" (Bull. European Assoc. Theoret. Comput. Sci. 68 (1999) 64-80).