New Upper Bounds in Klee’s Measure Problem

New upper bounds in Klee's measure problem (extended abstract)

New Upper Bounds for a Canonical Ramsey Problem

Let f (l; k) be the minimum n with the property that every coloring c : ? n+1] 2 Ramsey Theory studies the monochromatic subgraphs that are forced to appear in every k-coloring of the edges of K n. If we relax the requirement on the number of available colors, we can still ask what types of subgraphs are forced. Erd} os and Rado 1] formulated this question more precisely. Let N be the set of po...

New Upper Bounds for Maximum -

We develop and experiment with new upper bounds for the constrained maximum-entropy sampling problem. Our partition bounds are based on Fischer's inequality. Further new upper bounds combine the use of Fischer's inequality with previously developed bounds. We demonstrate this in detail by using the partitioning idea to strengthen the spectral bounds of Ko, Lee and Queyranne and of Lee. Computat...

New upper bounds of n!

We also proved that the approximation formula √ 2πn(n/e)neM [m] n for big factorials has a speed of convergence equal to n for m = 1,2,3,..., which give us a superiority over other known formulas by a suitable choice of m. Mathematics Subject Classification (2000): 41A60; 41A25; 57Q55; 33B15; 26D07.

New Upper Bounds for MaxSat

We describe exact algorithms that provide new upper bounds for the Maximum Satisfiability problem (MaxSat). We prove that MaxSat can be solved in time O(|F | · 1.3972), where |F | is the length of a formula F in conjunctive normal form and K is the number of clauses in F . We also prove the time bounds O(|F | · 1.3995), where k is the maximum number of satisfiable clauses, and O((1.1279) ) for ...