Significant research effort has been devoted in the study of approximation algorithms for NP-hard problems. Approximation algorithm for Max-Cut problem with performance guarantee of 0.87856 is long known. In this work we study balanced Max-Cut problem. We give a balancing factor β for given α

. This problem is NP-complete even for trees. We obtain the following new results using combinatorial approaches to the problem. (1) A polynomial time O(|V | 3/8)-approximation algorithm for the problem on graphs with girth at least six. (2) A polynomial time 2-approximation algorithm for the problem on trees

are exponential in worst case time complexity. We develop a two phase method where the first phase is a primal-dual type approximation algorithm that rapidly computes an initial feasible solution and the second phase is a refinement procedure that uses the dual of the LP relaxation of the winner determination

is to minimize the makespan of the schedule. SUM is an NP-hard problem even when the number of machines is defined to be m = 2. In this work, efficient approximation algorithms for SUM, when the number of machines is an arbitrary constant, are presented. The results hold for SUM and several extensions of SUM

of a customer it musts return to the depot for replenishment before continuing its route. The fixed routes problem can be modeled as a vehicle routing problem with stochastic demands, which in turn can be solved with a stochastic programming model with recourse. An effective and efficient approximate

The survivable network design problem is to construct a minimum-cost subgraph satisfying certain given edge-connectivity requirements. The first polynomial-time approximation algorithm was given by Williamson et al. [20]. This paper gives an improved version that is more efficient. Consider a graph

algorithms for the Hamming center problem. Our main result is a randomized ( 4 3 + ")-approximation algorithm running in polynomial time if the Hamming radius of S is at least superlogarithmic in k. Furthermore, we show how to nd in polynomial time a set B of O(log k) strings of length n

. Then, the scheduling problem is solved by a dual-approximation which leads to a simple structure of two consecutive shelves.

This paper presents an approximate algorithm for the winner determination problem in combinatorial auctions. This algorithm is based on limited discrepancy search (LDS). Internet auctions have become an integral part of Electronic Commerce and can incorporate large-scale, complicated types

that in the case where the value of a solution is the positive difference between the two partial sums, the problem is not 2 nk-approximable in polynomial time unless P=NP, for any constant k. In the positive direction, we give a polynomial-time algorithm that finds two subsets for which the difference of the two