M.L. Balinski. On finding integer solutions to linear programs. Proc. IBM Scientific Computing Symp. on Combinatorial Problems, 225-248. IBM, 1966.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... facility has a upper bound on the amount of demand it can serve, or softcapacitated facility location (each facility has a capacity, but we are allowed to open multiple copies of each facility) Facility location problems have occupied a central place in operations research since the early 60 s [2, 12, 14, 20, 17, 5, 7]. Many of these problems have been studied extensively from the perspective of approximation algorithms. Linear Programming (LP) based techniques have been applied successfully to uncapacitated and softcapacitated variants of the facility location problem to obtain constant factor approximation ....

M.L. Balinski. On finding integer solutions to linear programs. In Proc. IBM Scientific Computing Symposium on Combinatorial Problems, pages 225--248, 1966.

....balanced group strategyproof cost sharing mechanism for such games. Finding such a method for the facility location game seems particularly interesting. Recently, Goemans and Skutella [10] have studied this game and have a core allocation in case the well known LP relaxation, due to Balinski [1], has an integral solution. Finally, we consider the purely combinatorial question of characterizing the space of cross monotone methods corresponding to a given nondecreasing submodular function. We show that this is a polyhedron and characterize a subset of its corner points. We leave the open ....

....is that the optimal cost function does not exhibit the covering property. For an instance, consider a cycle on 6 vertices, with 3 cities and 3 facilities alternating. The cost of each edge is 1 and the cost of opening each facility is 2. Awell known LP relaxation for this problem, due to Balinski [1], is given below. Several constant factor approximation algorithms are based on this relaxation. Suppose C is the set of cities and F is the set of facilities. Suppose f i is the cost of opening facility i and c ij is the cost of connecting city j to facility i. In the corresponding integer ....

M. L. Balinski. On finding integer solutions to linear programs. In Proc. IBM Scientific Computing Symp. on Combinatorial Problems, pages 225--248, 1966.

....a game theoretic setting since all users are being served. Their definition of fairness is that no subset of users be charged more than the cost of serving this subset optimally. They give a budget balanced and fair cost allocation only for instances for which the LP relaxation (due to Balinski [1]) of this problem has an integral optimal solution. The latter restriction is quite severe. Our definition of No Subsidy is inspired by their work. 2 The model For convenience, let us consider the setting of multicasting for giving the basic definitions and theorems; they are of course valid in ....

M. L. Balinski. On finding integer solutions to linear programs. Proc. IBM Scientific Computing Symp. on Combinatorial Problems, 225-248. IBM, 1966.

....that should get service. We provide generalizations of various approximation algorithms to deal with this added constraint. 1 Introduction The facility location problem and the related clustering problems, k median and k center, are widely studied in operations research and computer science [3, 7, 22, 24, 32]. Typically in problems of this type, we are given an n vertex graph whose edge weights define a distance metric. Let c ij denote the distance between nodes i and j. In the (uncapacitated) facility location problem, each node i is associated with a facility cost f i , which reflects the cost of ....

M. L. Balinski, "On finding integer solutions to linear programs", Proc. of the IBM Scientific Computing Symposium on Combinatorial Problems, pages 225-- 248, (1966).

....Plaxton and Rajaraman [6] have shown that the local search heuristic proposed by Kuehn and Hamburger [7] achieves a constant approximation for many variants of the UFL problem. Uncapacitated facility location (UFL) problems have been widely studied in the Operations Research literature (see [1, 7, 10, 15]) This problem has been studied from different perspectives, as clustering analysis [12] machine scheduling and information retrieval, communication networks [11] and many others. For an extensive survey of closely related work one can read the chapter by Cornuejols, Nemhauser and Wolsey [2] ....

....symmetric and satisfy the triangle inequality. We wish to find an assignment of each location in D to an open facility so as to minimize the total cost incurred. This is the uncapacitated facility location problem (UFL) We can state the above problem as an integer programming problem as in [14, 1]. There is a 0 1 variable y i ; i 2 F indicating if a facility is open at location i. The 0 1 variable x ij ; i 2 F; j 2 D indicates if client j is assigned to the facility at i. min X i2F f i y i X i2F X j2D d j c ij x ij subject to X i2F x ij = 1 for each j 2 D x ij y i for each i ....

M. L. Balinski, "On finding integer solutions to linear programs", Proc. of the IBM Scientific Computing Symposium on Combinatorial Problems, pages 225-- 248, (1966).

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M.L. Balinski. On finding integer solutions to linear programs. Proc. IBM Scientific Computing Symp. on Combinatorial Problems, 225-248. IBM, 1966.

No context found.

M. Balinski. On finding integer solutions to linear programs. In Proc. IBM Scientific Computing Symp. on Combinatorial Problems, 225--248, 1966.

No context found.

M. L. Balinski. On finding integer solutions to linear programs. In Proc. IBM Scientific Computing Symp. on Combinatorial Problems, pages 225-- 248, 1966.

No context found.

M. L. Balinski. On finding integer solutions to linear programs. Proc. IBM Scientific Computing Symp. on Combinatorial Problems, 225-248. IBM, 1966.

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