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Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the(More)
We consider the following integer feasibility problem: Given positive integer numbers a0 a1 an, with gcd a1 an = 1 and a = a1 an , does there exist a vector x ∈ n≥0 satisfying a x = a0? We prove that if the coefficients a1 an have a certain decomposable structure, then the Frobenius number associated with a1 an, i.e., the largest value of a0 for which a x=(More)
We consider the polyhedral approach to solving the capacitated facility location problem. The valid inequalities considered are the knapsack, ow cover, e ective capacity, single depot, and combinatorial inequalities. The ow cover, e ective capacity, and single depot inequalities form subfamilies of the general family of submodular inequalities. The(More)
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 0rst survey their use in integer programming, presenting among others Lenstra’s algorithm that is polynomial in 0xed dimension, and the solution of diophanine equations using basis reduction. The second topic(More)
On August we completed the factorization of the bit digit number RSA with the help of the Number Field Sieve factoring method NFS This is a new record for factoring general numbers Moreover bit RSA keys are frequently used for the protection of electronic commerce at least outside the USA so this factorization represents a breakthrough in research on RSA(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 yand z-facilities each client should be assigned, in order to satisfy the demand at maximum profit. We first present two(More)