The paper presents a general method of designing onstant-fa tor approximation algorithms for some dis rete optimization problems with assignment-type onstraints. The ore of the method is a simpleâ€¦ (More)

In this paper, we obtain an (1 âˆ’ eâˆ’1)-approximation algorithm for maximizing a nondecreasing submodular set function subject to a knapsack constraint. This algorithm requires O(n) function valueâ€¦ (More)

A separable assignment problem (SAP) is defined by a set of bins and a set of items to pack in each bin; a value, fij, for assigning item j to bin i; and a separate packing constraint for each bin -â€¦ (More)

We consider the following problem: The Santa Claus has n presents that he wants to distribute among m kids. Each kid has an arbitrary value for each present. Let p<sub>ij</sub> be the value that kidâ€¦ (More)

We consider the problem of schedulingjobs with release dates onm machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemesâ€¦ (More)

We study the multidimensional generalization of the classical Bin Packing problem: Given a collection of d-dimensional rectangles of specified sizes, the goal is to pack them into the minimum numberâ€¦ (More)

In this paper we introduce a new general framework for set covering problems, based on the combination of randomized rounding of the (near-)optimal solution of the linear programming (LP) relaxation,â€¦ (More)