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  • 1
    Title: Parallel processing of discrete optimization problems : DIMACS workshop, April 28-29, 1994; 22
    Contributer: Pardalos, Panos M. , Resende, Mauricio G. C. , Ramakrishnan, K. G.
    Publisher: Providence, RI :AMS,
    Year of publication: 1995
    Pages: 374 S.
    Series Statement: DIMACS Series in Discrete Mathematics and Theoretical Computer Science 22
    Type of Medium: Book
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 52 (1991), S. 555-586 
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper gives computational results for an efficient implementation of a variant of dual projective algorithm for linear programming. The implementation uses the preconditioned conjugate gradient method for computing projections. Our computational experience reported in this paper indicates that this algorithm has potential as an alternative for solving very large LPs in which the direct methods fail due to memory and CPU time requirements. The conjugate gradient algorithm was able to find very accurate directions even when the system was ill-conditioned. The paper also discusses a new mathematical technique called the reciprocal estimates for estimating the primal variables. We have conducted extensive computational experiments on problems representative of large classes of applications of current interest. We have also chosen instances of the problems of future potential interest, which could not be solved in the past due to the weakness of the prior solution methods, but which represent a large class of new applications. The hypergraph model is such an example. Comparison of our implementation with MINOS 5.1 shows that our implementation is orders of magnitude faster than MINOS 5.1 for these problems.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 52 (1991), S. 597-618 
    ISSN: 1436-4646
    Keywords: Integer programming ; interior point method ; Steiner triple systems ; set covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present an interior point approach to the zero–one integer programming feasibility problem based on the minimization of a nonconvex potential function. Given a polytope defined by a set of linear inequalities, this procedure generates a sequence of strict interior points of this polytope, such that each consecutive point reduces the value of the potential function. An integer solution (not necessarily feasible) is generated at each iteration by a rounding scheme. The direction used to determine the new iterate is computed by solving a nonconvex quadratic program on an ellipsoid. We illustrate the approach by considering a class of difficult set covering problems that arise from computing the 1-width of the incidence matrix of Steiner triple systems.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 57 (1992), S. 215-238 
    ISSN: 1436-4646
    Keywords: Inductive inference ; Boolean function synthesis ; satisfiability ; artificial intelligence ; integer programming ; interior point method ; Riemannian geometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean functionℱ:{0, 1} n → {0, 1} using outputs obtained by applying a limited number of random inputs to the hidden function. Given this input—output sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used for defining the search region is dynamically modified. Computational results on 8-, 16- and 32-input, 1-output functions are presented. Our implementation successfully identified the majority of hidden functions in the experiment.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1572-9338
    Keywords: Integer programming ; interior point method ; logic ; satisfiability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We apply the zero-one integer programming algorithm described in Karmarkar [12] and Karmarkar, Resende and Ramakrishnan [13] to solve randomly generated instances of the satisfiability problem (SAT). The interior point algorithm is briefly reviewed and shown to be easily adapted to solve large instances of SAT. Hundreds of instances of SAT (having from 100 to 1000 variables and 100 to 32,000 clauses) are randomly generated and solved. For comparison, we attempt to solve the problems via linear programming relaxation with MINOS.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Telecommunication systems 4 (1995), S. 151-175 
    ISSN: 1572-9451
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Caller I.D. service, whereby the telephone number of the calling party is visually displayed to the called party during ringing, is now available in some areas of the U.S., but it is restricted to calls within a local calling area, and for which the calling and called party are customers of the same local telephone company. If Caller I.D. service is extended nationwide, identification of a long-distance call will, in a typical case, require the participation of three companies: the local exchange carrier originating the call, the long-distance carrier, and the local exchange carrier terminating the call. How shall the revenues from the service be divided among the participating firms? We apply cooperative game theory to address this question.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 50 (1994), S. 387-410 
    ISSN: 1572-9338
    Keywords: Quadratic assignment problem ; branch-and-bound ; lower bound ; combinatorial optimization ; AMS(MOS) 68Q25 ; 90B80 ; 90C27
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We investigate the classical Gilmore-Lawler lower bound for the quadratic assignment problem. We provide evidence of the difficulty of improving the Gilmore-Lawler bound and develop new bounds by means of optimal reduction schemes. Computational results are reported indicating that the new lower bounds have advantages over previous bounds and can be used in a branch-and-bound type algorithm for the quadratic assignment problem.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1572-9443
    Keywords: Asymptotics ; adaptive windows ; access control ; bursty sources ; buffer management ; retransmission protocols
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper we articulate our philosophy and approach to the design and control of high speed data networks. The object is to put into perspective and to explain the coordination of various isolated pieces of detailed technical analyses that have been reported in several recent papers. In the process we summarize what we have learnt in our recent work and, also, we give indications of the direction of our future work. Our scheme integrates feedback and open loop control. The feedback control is exercised by sliding windows; access controllers regulate bursty sources. All our design proposals are rooted in asymptotic analyses; the justification for asymptotics comes from the largeness of the parameters, such as propagation delay, speed, window size, buffer size, and the number of virtual circuits. This analysis makes a strong case for operating in a specific “moderate usage” regime, and adaptive dynamic windowing algorithms are given that make this happen; moreover, when in this regime, buffers may be sized aggressively small without jeopardizing performance and the simplicity of the retransmission protocol. The topics in the paper are: model of communication, results on the steady-state behavior of the basic model, access control, small buffers and retransmission protocols, dynamic adaptive windows, bursty sources, and contrast with previous work.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 11 (1976), S. 50-66 
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An improved version of an unconstrained optimization algorithm based upon a homogeneous function is presented. The method is numerically stable and uses the Bartels—Golub factorization instead of Householder's modification formula. Several numerical tests indicate that the proposed method is robust and very efficient.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Computational optimization and applications 2 (1993), S. 261-271 
    ISSN: 1573-2894
    Keywords: Computational experimentation ; linear assignment problem ; random variables ; interior point methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In the paper, we study the expected optimal value of random linear assignment problems, whose data are random variables with the uniform and the exponential distributions. An interior point approach is used to solve large-scale dense assignment problems with size up to 10,000 nodes and 100 million edges. Our computational results indicate the validity of a long-standing conjecture about the limiting value of the expected optimal assignment. Some interesting open problems and extensions are discussed.
    Type of Medium: Electronic Resource
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