We analyze the addition of a simple local improvement step to various known ran-domized approximation algorithms. Let ' 0:87856 denote the best approximation ratio currently known for the Max Cut problem on general graphs GW95]. We consider a semideenite relaxation of the Max Cut problem, round it using the random hyperplane rounding technique of ((GW95]), and then add a local improvement step....

This paper studies the existence of eecient (small size) ampliiers for proving explicit inaproximability results for bounded degree and bounded occurrence combinatorial optimization problems, and gives an explicit construction for such ampliiers. We use this construction to improve the currently best known approximation lower bounds for bounded occurrence instances of linear equations mod 2, an...

Metric MAX-CUT is the problem of dividing a set of points in metric space into two parts so as to maximize the sum of the distances between points belonging to distinct parts. We show that metric MAX-CUT has a polynomial time randomized approximation scheme.

This paper gives a straightforward implementation of simulated annealing for solving maximum cut problems and compare its performance to that of some existing heuristic solvers. The formulation used is classical, dating to a 1989 paper of Johnson, Aragon, McGeoch, and Schevon. This implementation uses no structure peculiar to the maximum cut problem, but its low per-iteration cost allows it to ...

We present a sequent calculus for intuitionistic non-commutative linear logic (INCLL), show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cut-free derivations, and arbitrary natural deductions to sequent derivations with cut. This gives us a syntactic proof of normalization for...