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  • A maximum edge-weight clique extraction algorithm based on branch-and-bound
    Discret. Optim. (IF 0.815) Pub Date : 2020-05-18
    Satoshi Shimizu; Kazuaki Yamaguchi; Sumio Masuda

    The maximum edge-weight clique problem is to find a clique whose sum of edge-weight is the maximum for a given edge-weighted undirected graph. The problem is NP-hard and some branch-and-bound algorithms have been proposed. In this paper, we propose a new exact algorithm based on the branch-and-bound method. It assigns edge-weights to vertices and calculates upper bounds using vertex coloring. By some

    更新日期:2020-05-18
  • Spectral aspects of symmetric matrix signings
    Discret. Optim. (IF 0.815) Pub Date : 2020-04-30
    Charles Carlson; Karthekeyan Chandrasekaran; Hsien-Chih Chang; Naonori Kakimura; Alexandra Kolla

    The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of finding symmetric signings of matrices with natural spectral properties. Our results are the following: 1. We characterize matrices that have an invertible signing: a symmetric matrix has an invertible symmetric signing if and

    更新日期:2020-04-30
  • The reach of axis-aligned squares in the plane
    Discret. Optim. (IF 0.815) Pub Date : 2020-04-18
    Hugo A. Akitaya; Matthew D. Jones; David Stalfa; Csaba D. Tóth

    Given a set S of n points in the unit square U=[0,1]2, an axis aligned square r⊆U is anchored at S if a corner of r is in S, and empty if no point in S lies in the interior of r. The reach R(S) of S is the union of all anchored empty squares for S. The maximum area of a packing of U with anchored empty squares is bounded above by area(R(S)). We prove that area(R(S))≥12 for every nonempty finite set

    更新日期:2020-04-18
  • A cut-and-branch algorithm for the Quadratic Knapsack Problem
    Discret. Optim. (IF 0.815) Pub Date : 2020-03-04
    Franklin Djeumou Fomeni; Konstantinos Kaparis; Adam N. Letchford

    The Quadratic Knapsack Problem (QKP) is a well-known NP-hard combinatorial optimisation problem, with many practical applications. We present a ‘cut-and-branch’ algorithm for the QKP, in which a cutting-plane phase is followed by a branch-and-bound phase. The cutting-plane phase is more sophisticated than the existing ones in the literature, incorporating several classes of cutting planes, two primal

    更新日期:2020-03-04
  • On inequalities with bounded coefficients and pitch for the min knapsack polytope
    Discret. Optim. (IF 0.815) Pub Date : 2020-02-29
    Daniel Bienstock; Yuri Faenza; Igor Malinović; Monaldo Mastrolilli; Ola Svensson; Mark Zuckerberg

    The min knapsack problem appears as a major component in the structure of capacitated covering problems. Its polyhedral relaxations have been extensively studied, leading to strong relaxations for networking, scheduling and facility location problems. A valid inequality αTx≥α0 with α≥0 for a min knapsack instance is said to have pitch ≤π (π a positive integer) if the π smallest strictly positive αj

    更新日期:2020-02-29
  • Circuit walks in integral polyhedra
    Discret. Optim. (IF 0.815) Pub Date : 2020-01-15
    Steffen Borgwardt; Charles Viss

    Circuits play a fundamental role in the theory of linear programming due to their intimate connection to algorithms of combinatorial optimization and the efficiency of the simplex method. We are interested in better understanding the properties of circuit walks in integral polyhedra. In this paper, we introduce a hierarchy for integral polyhedra based on different types of behavior exhibited by their

    更新日期:2020-01-15
  • On the complexity of solving a decision problem with flow-depending costs: The case of the IJsselmeer dikes
    Discret. Optim. (IF 0.815) Pub Date : 2020-01-08
    A. Abiad; S. Gribling; D. Lahaye; M. Mnich; G. Regts; L. Vena; G. Verweij; P. Zwaneveld

    We consider a fundamental integer programming (IP) model for cost–benefit analysis and flood protection through dike building in the Netherlands, due to Zwaneveld and Verweij (2017). Experimental analysis with data for the IJsselmeer shows that the solution of the linear programming relaxation of the IP model is integral. This naturally leads to question whether the polytope associated to the IP is

    更新日期:2020-01-08
  • Quality of equilibria for selfish bin packing with cost sharing variants
    Discret. Optim. (IF 0.815) Pub Date : 2019-11-14
    György Dósa; Leah Epstein

    Bin packing is the problem of splitting a set of items into a minimum number of subsets, called bins, of total sizes no larger than 1, where a solution is called a packing. We study bin packing games where an item also has a positive weight, and given a valid packing of the items, each item has a cost associated with it, such that the cost of an item is the ratio between its weight and the total weight

    更新日期:2019-11-14
  • On the intrinsic volumes of intersections of congruent balls
    Discret. Optim. (IF 0.815) Pub Date : 2019-03-20
    Károly Bezdek

    Let Ed denote the d-dimensional Euclidean space. The r-ball body generated by a given set in Ed is the intersection of balls of radius r centered at the points of the given set. In this paper we prove the following Blaschke–Santaló-type inequalities for r-ball bodies: for all 1≤k≤d and for any set of given volume in Ed the kth intrinsic volume of the r-ball body generated by the set becomes maximal

    更新日期:2019-03-20
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