Optimal myopic algorithms for random 3-SAT - Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on
نویسندگان
چکیده
Let F3(n, m) be a random 3-SAT formula formed by selecting uniformly, independently, and with replacement, m clauses among all 8 ( y ) possible 3-clauses over n variables. It has been conjectured that there exists a constant 7-3 such that for any E > 0, F3(n, (r3 e)n) is almost surely satisfiable, but F3 (n, ( 7 3 + E).) is almost surely unsatisjiable. The best lower bounds for the potential value of r3 have come from analyzing rather simple extensions of unit-clause propagation. Recently, it was shown [2] that all these extensions can be cast in a common framework and analyzed in a uniform manner by employing differential equations. Here, we determine optimal algorithms expressible in that framework, establishing r3 > 3.26. We extend the analysis via differential equations, and make extensive use of a new optimization problem we call ‘“ax-density multiple-choice knapsack ”. The structure of optimal knapsack solutions elegantly characterizes the choices made by an optimal algorithm.
منابع مشابه
Fast Universalization of Investment Strategies
A universalization of a parameterized investment strategy is an online algorithm whose average daily performance approaches that of the strategy operating with the optimal parameters determined offline in hindsight. We present a general framework for universalizing investment strategies and discuss conditions under which investment strategies are universalizable. We present examples of common i...
متن کاملA DNA-Based Random Walk Method for Solving k-SAT
This paper presents implementation of a concurrent version of Schöning’s algorithm for k-SAT (Proceedings of 40th Symposium on Foundations of Computer Science, pages 410–414. IEEE Computer Society Press, Los Alamitos, CA, 1999). It is shown that the algorithm can be implemented with space complexity O((2− 2 k ) ) and time complexity O(mn), where n is the number of variables and m is that of cla...
متن کاملCommunication-optimal maintenance of replicated information - Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on
متن کامل
RNA-Folding - From Hardness to Algorithms
This is an overview of the invited talk delivered at the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS-2016). 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
متن کاملOptimal Reachability in Weighted Timed Automata and Games
This is an overview of the invited talk delivered at the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS-2016). 1998 ACM Subject Classification F.1.1 Models of Computation – D.2.4 Software/Program Verification
متن کامل