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  • ddc:000  (1)
  • rounding fractional solutions  (1)
  • 1
    Electronic Resource
    Electronic Resource
    A note on the prize collecting traveling salesman problem (1993)
    Springer
    Mathematical programming 59 (1993), S. 413-420 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; prize collecting ; rounding fractional solutions ; traveling salesman problem ; worst-case analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study the version of the prize collecting traveling salesman problem, where the objective is to find a tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. We present an approximation algorithm with constant bound. The algorithm is based on Christofides' algorithm for the traveling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers, feasible for the original problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581256
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    Paper (German National Licenses)
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  • 2
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    Capacitated Network Design with Multicast Commodities (2000)
    Details
    Publication Date: 2014-02-26
    Description: This paper addresses the problem of designing a minimum cost network whose capacities are sufficiently large to allow a feasible routing of a given set of multicast commodities. A multicast commodity consists of a set of two or mo re terminals that need to be connected by a so called broadcast tree, which consumes on all of its edges a capacity as large as the demand value associated with that commodity. We model the network design problem with multicast commodities as the problem of packing capacitated Steiner trees in a graph. In the first part of the paper we present three mixed-integer programming formulations for this problem. The first natural formulation uses only one integer capacity variable for each edge and and one binary tree variable for each commodity-edge pair. Applying well-known techniques from the Steiner tree problem, we then develop a stronger directed and a multicommodity flow based mixed-integer programming formulation. In the second part of the paper we study the associated polyhedra and derive valid and even facet defining inequalities for the natural formulation. Finally, we describe separation algorithms for these inequalities and present computational results that demonstrate the strength of our extended formulations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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