We present new approximation algorithms for several facility location problems. In each facility location problem that we study, there is a set of locations at which we may build a facility (such as a warehouse), where the cost of building at location i is ~i; ftier-more, there is a set of client locations (such as stores) that require to be serviced by a… (More)
We consider the following integer feasibility problem: Given positive integer numbers a 0 a 1 a n , with gcda 1 a n = 1 and a = a 1 a n , does there exist a vector x ∈ n ≥0 satisfying a x = a 0 ? We prove that if the coefficients a 1 a n have a certain decomposable structure, then the Frobenius number associated with a 1 a n , i.e., the largest value of a 0… (More)
We consider the polyhedral approach to solving the capacitated facility location problem. The valid inequalities considered are the knapsack, ow cover, eeective capacity, single depot, and combinatorial inequalities. The ow cover, eeective capacity, and single depot inequalities form subfamilies of the general family of submodular inequalities. The… (More)
This paper reports on the factorization of the 512–bit number RSA–155 by the Number Field Sieve factoring method (NFS) and discusses the implications for RSA.
In the k-level uncapacitated facility location problem, we have a set of demand points where clients are located. The demand of each client is known. Facilities have to be located at given sites in order to service the clients, and each client is to be serviced by a sequence of k different facilities, each of which belongs to a distinct level. There are no… (More)
In this survey we address three of the principal algebraic approaches to integer programming. After introducing lattices and basis reduction, we ÿrst survey their use in integer programming, presenting among others Lenstra's algorithm that is polynomial in ÿxed dimension, and the solution of diophanine equations using basis reduction. The second topic… (More)
We study the two-level uncapacitated facility location (TUFL) problem. Given two types of facilities, which we call y-facilities and z-facilities, the problem is to decide which facilities of both types to open, and to which pair of y-and z-facilities each client should be assigned, in order to satisfy the demand at maximum proot. We rst present two… (More)