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  • Minimum energy configurations on a toric lattice as a quadratic assignment problem
    Discret. Optim. (IF 0.824) Pub Date : 2020-10-19
    Daniel Brosch; Etienne de Klerk

    We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex quadratic programming (CQP), and a semidefinite programming (SDP) bound. Since the last two bounds were not compared directly before, we prove that the SDP bound is stronger than the CQP bound. We then apply these to improve known bounds on a discrete energy minimization problem, reformulated as a QAP

    更新日期:2020-10-19
  • Scheduling split intervals with non-uniform demands
    Discret. Optim. (IF 0.824) Pub Date : 2020-08-28
    Venkatesan T. Chakaravarthy, Anamitra R. Choudhury, Sambuddha Roy, Yogish Sabharwal

    We study the problem of maximizing the throughput of jobs wherein each job consists of multiple tasks. Consider a system offering a capacity of one unit. We are given a set of jobs, each consisting of a sequence of r tasks. Each task is associated with a demand and an interval where it should be scheduled. Each job has a profit associated with it. The objective is to select a subset of jobs having

    更新日期:2020-08-28
  • BDD-based optimization for the quadratic stable set problem
    Discret. Optim. (IF 0.824) Pub Date : 2020-08-27
    Jaime E. González; Andre A. Cire; Andrea Lodi; Louis-Martin Rousseau

    The quadratic stable set problem (QSSP) is a natural extension of the well-known maximum stable set problem. The QSSP is NP-hard and can be formulated as a binary quadratic program, which makes it an interesting case study to be tackled from different optimization paradigms. In this paper, we propose a novel representation for the QSSP through binary decision diagrams (BDDs) and adapt a hybrid optimization

    更新日期:2020-08-27
  • A convex cover for closed unit curves has area at least 0.1
    Discret. Optim. (IF 0.824) Pub Date : 2020-08-25
    Bogdan Grechuk, Sittichoke Som-am

    We improve a lower bound for the smallest area of convex covers for closed unit curves from 0.0975 to 0.1, which makes it substantially closer to the current best upper bound 0.11023. We did this by considering the minimal area of convex hull of circle, line of length 12, and rectangle with side 0.1727×0.3273. By using geometric methods and the Box-search algorithm, we proved that this area is at least

    更新日期:2020-08-25
  • On the edge capacitated Steiner tree problem
    Discret. Optim. (IF 0.824) Pub Date : 2020-08-17
    Cédric Bentz, Marie-Christine Costa, Alain Hertz

    Given a graph G=(V,E) with a root r∈V, positive capacities {c(e)|e∈E}, and non-negative lengths {ℓ(e)|e∈E}, the minimum-length (rooted) edge capacitated Steiner tree problem is to find a tree in G of minimum total length, rooted at r, spanning a given subset T⊂V of vertices, and such that, for each e∈E, there are at most c(e) paths, linking r to vertices in T, that contain e. We study the complexity

    更新日期:2020-08-17
  • Fashion game on graphs
    Discret. Optim. (IF 0.824) Pub Date : 2020-08-07
    Chenli Shen, Wensong Lin

    In this paper, we propose and study an optimization problem of the fashion game on graphs, which can be regarded as a graph extension of matching pennies. There are two kinds of players in a graph G: Conformists and Rebels. All players choose their actions from an identical set of the two symmetric actions, say {0,1}. An action profile π of G is a mapping from the vertex set of G to the action set

    更新日期:2020-08-07
  • Single-machine scheduling with maintenance activities and rejection
    Discret. Optim. (IF 0.824) Pub Date : 2020-08-03
    Juan Zou, Jinjiang Yuan

    We study the single-machine scheduling with job rejection and the additional constraint that a maintenance activity of fixed length must be performed either by a deadline or in a fixed time interval. The scheduling costs of the accepted jobs are the makespan, maximum lateness, maximum tardiness, maximum weighted completion time, total (weighted) completion time, and total (weighted) number of tardy

    更新日期:2020-08-03
  • Integer programming in parameterized complexity: Five miniatures
    Discret. Optim. (IF 0.824) Pub Date : 2020-07-20
    Tomáš Gavenčiak; Martin Koutecký; Dušan Knop

    Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity. However, our perception is that, except for Lenstra’s algorithm for solving integer linear programming in fixed dimension, there is still little understanding in the parameterized complexity community of the strengths and limitations of the available tools. This is understandable:

    更新日期:2020-07-20
  • Decentralized algorithms for distributed integer programming problems with a coupling cardinality constraint
    Discret. Optim. (IF 0.824) Pub Date : 2020-07-15
    Ezgi Karabulut, Shabbir Ahmed, George Nemhauser

    We consider a multi-player optimization where each player has her own optimization problem and the individual problems are connected by a cardinality constraint on their shared resources. We give distributed algorithms that allow each player to solve their own optimization problem and still achieve a global optimization solution for problems that possess a concavity property. For problems without the

    更新日期:2020-07-15
  • Penalty and partitioning techniques to improve performance of QUBO solvers
    Discret. Optim. (IF 0.824) Pub Date : 2020-06-29
    Amit Verma; Mark Lewis

    Quadratic Unconstrained Binary Optimization (QUBO) modeling has become a unifying framework for solving a wide variety of both unconstrained as well as constrained optimization problems. More recently, QUBO (or equivalent −1∕+1 Ising Spin) models are a requirement for quantum annealing computers. Noisy Intermediate-Scale Quantum (NISQ) computing refers to classical computing preparing or compiling

    更新日期:2020-06-29
  • Linear programming based approximation for unweighted induced matchings—Breaking the Δ barrier
    Discret. Optim. (IF 0.824) Pub Date : 2020-06-18
    Julien Baste, Maximilian Fürst, Dieter Rautenbach

    A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (2018) provide an approximation algorithm with ratio Δ for the weighted version of the induced matching problem on graphs of maximum degree Δ. Their approach is based on an integer linear programming formulation whose integrality gap is at least Δ−1

    更新日期:2020-06-18
  • The Aα spectral radius and maximum outdegree of irregular digraphs
    Discret. Optim. (IF 0.824) Pub Date : 2020-06-05
    Weige Xi, Ligong Wang

    Let G be a digraph with adjacency matrix A(G). Let D(G) be the diagonal matrix with outdegrees of vertices of G. In this paper, we study the convex linear combinations of A(G) and D(G), defined as Aα(G)=αD(G)+(1−α)A(G),0≤α≤1. The largest modulus of the eigenvalues of Aα(G), is called the Aα spectral radius of G, denoted by λα(G). We establish some lower bounds on Δ+−λα(G) for strongly connected irregular

    更新日期:2020-06-05
  • A maximum edge-weight clique extraction algorithm based on branch-and-bound
    Discret. Optim. (IF 0.824) 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
  • The nestedness property of the convex ordered median location problem on a tree
    Discret. Optim. (IF 0.824) Pub Date : 2020-04-30
    Mark Rozanov, Arie Tamir

    This paper deals with the problem of locating an extensive facility of restricted length within a given tree network. Topologically, the selected extensive facility is a subtree. The nestedness property means that a solution of a problem with a shorter length constraint is part of a solution of the same problem with a longer length constraint. We prove the existence of a nestedness property for a common

    更新日期:2020-04-30
  • Spectral aspects of symmetric matrix signings
    Discret. Optim. (IF 0.824) 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 0.824) 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
  • The stable marriage problem with ties and restricted edges
    Discret. Optim. (IF 0.824) Pub Date : 2020-03-04
    Ágnes Cseh, Klaus Heeger

    In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of agents, who mutually prefer each other to their respective partner. Ties in the preferences allow for three different definitions for a stable matching: weak, strong

    更新日期:2020-03-04
  • A cut-and-branch algorithm for the Quadratic Knapsack Problem
    Discret. Optim. (IF 0.824) 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 0.824) 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
  • On the Balanced Minimum Evolution polytope
    Discret. Optim. (IF 0.824) Pub Date : 2020-02-26
    Daniele Catanzaro, Raffaele Pesenti, Laurence Wolsey

    Recent advances on the polyhedral combinatorics of the Balanced Minimum Evolution Problem (BMEP) enabled the characterization of a number of facets of its convex hull (also referred to as the BMEP polytope) as well as the discovery of connections between this polytope and the permutoassociahedron. In this article, we extend these studies, by presenting new results concerning some fundamental characteristics

    更新日期:2020-02-26
  • Extended formulations for convex hulls of some bilinear functions
    Discret. Optim. (IF 0.824) Pub Date : 2020-02-15
    Akshay Gupte, Thomas Kalinowski, Fabian Rigterink, Hamish Waterer

    We consider the problem of characterizing the convex hull of the graph of a bilinear function f on the n-dimensional unit cube [0,1]n. Extended formulations for this convex hull are obtained by taking subsets of the facets of the Boolean Quadric Polytope (BQP). Extending existing results, we propose a systematic study of properties of f that guarantee that certain classes of BQP facets are sufficient

    更新日期:2020-02-15
  • Partial immunization of trees
    Discret. Optim. (IF 0.824) Pub Date : 2020-02-06
    Mitre C. Dourado, Stefan Ehard, Lucia D. Penso, Dieter Rautenbach

    For a graph G and a non-negative integer-valued function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We study the problem of maximizing the minimum order of a dynamic monopoly by increasing the threshold values of individual vertices subject to vertex-dependent

    更新日期:2020-02-06
  • Circuit walks in integral polyhedra
    Discret. Optim. (IF 0.824) 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 0.824) 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 0.824) 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
  • Capacitated Multi-Layer Network Design with Unsplittable Demands: Polyhedra and Branch-and-Cut
    Discret. Optim. (IF 0.824) Pub Date : 2019-10-18
    Amal Benhamiche, A. Ridha Mahjoub, Nancy Perrot, Eduardo Uchoa

    We consider the Capacitated Multi-Layer Network Design with Unsplittable demands (CMLND-U) problem. Given a two-layer network and a set of traffic demands, this problem consists in installing minimum cost capacities on the upper layer so that each demand is routed along a unique “virtual” path (even using a unique capacity on each link) in this layer, and each installed capacity is in turn associated

    更新日期:2019-10-18
  • Linear-time algorithms for finding Hamiltonian and longest (s,t)-paths in C-shaped grid graphs
    Discret. Optim. (IF 0.824) Pub Date : 2019-09-03
    Fatemeh Keshavarz-Kohjerdi, Alireza Bagheri

    The longest and Hamiltonian path problems are well-known NP-hard problems in graph theory. Despite many applications of these problems, they are still open for many classes of graphs, including solid grid graphs and grid graphs with some holes. We consider the longest and Hamiltonian (s,t)-path problems in C-shaped grid graphs. A (s,t)-path is a path between two given vertices s and t of the graph

    更新日期:2019-09-03
  • Disjoint dominating and 2-dominating sets in graphs
    Discret. Optim. (IF 0.824) Pub Date : 2019-08-22
    Mateusz Miotk, Jerzy Topp, Paweł Żyliński

    A subset D⊆VG is a dominating set of G if every vertex in VG−D has a neighbor in D, while D is 2-dominating if every vertex in VG−D has at least two neighbors in D. A graph G is a DD2-graph if it has a pair (D,D2) of disjoint subsets of vertices such that D is a dominating set, and D2 is a 2-dominating set of G. Studies of first properties of the DD2-graphs were initiated by Henning and Rall (2013)

    更新日期:2019-08-22
  • Separation of cycle inequalities in periodic timetabling
    Discret. Optim. (IF 0.824) Pub Date : 2019-08-20
    Ralf Borndörfer, Heide Hoppmann, Marika Karbstein, Niels Lindner

    Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem in public transport. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we contribute a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. Moreover, we provide several NP-completeness results, indicating that pseudo-polynomial

    更新日期:2019-08-20
  • Multiple Bipartite Complete Matching Vertex Blocker Problem: Complexity, polyhedral analysis and Branch-and-Cut
    Discret. Optim. (IF 0.824) Pub Date : 2019-08-06
    Pierre Laroche, Franc Marchetti, Sébastien Martin, Anass Nagih, Zsuzsanna Róka

    Given a bipartite graph G=(U∪V,E), |U|⩽|V|, the surplus of G is defined by the maximum number k such that a matching covering all vertices of U still exists upon removal of any k vertices from V. Given a partition U={U1,…,Um} of U, the Multiple Bipartite Complete Matching Vertex Blocker Problem (MBCMVBP) consists in finding a partition V={V1,…,Vm} of V such that the smallest surplus among those of

    更新日期:2019-08-06
  • Minimum diameter color-spanning sets revisited
    Discret. Optim. (IF 0.824) Pub Date : 2019-07-12
    Jonas Pruente

    We address point sets in the d-dimensional space, in which every point is colored with at least one color out of the set C. A Color-Spanning Set or Rainbow Set is a set of points that covers all colors of C. The diameter of a set is the maximum distance between two points in the set. In this paper we answer some open questions about Minimum Diameter Color-Spanning Sets in d-dimensional space, which

    更新日期:2019-07-12
  • Single-machine scheduling with positional due indices and positional deadlines
    Discret. Optim. (IF 0.824) Pub Date : 2019-07-08
    Rubing Chen, Jinjiang Yuan, Lingfa Lu

    In this paper, we study single-machine scheduling problems with due dates, positional due indices, deadlines and positional deadlines. The scheduling criteria studied in this paper include the number of position-violated tasks, the weighted number of position-violated tasks, and the maximum positional lateness of tasks, by also combining with other traditional scheduling criteria. For each problem

    更新日期:2019-07-08
  • Small 1-defective Ramsey numbers in perfect graphs
    Discret. Optim. (IF 0.824) Pub Date : 2019-06-18
    Tınaz Ekim, John Gimbel, Oylum Şeker

    In this paper, we initiate the study of defective Ramsey numbers for the class of perfect graphs. Let PG be the class of all perfect graphs and R1PG(i,j) denote the smallest n such that all perfect graphs on n vertices have either a 1-dense i-set or a 1-sparse j-set. We show that R1PG(3,j)=j for any j≥2, R1PG(4,4)=6, R1PG(4,5)=8, R1PG(4,6)=10, R1PG(4,7)=13, R1PG(4,8)=15 and R1PG(5,5)=13. We exhibit

    更新日期:2019-06-18
  • On some tractable and hard instances for partial incentives and target set selection
    Discret. Optim. (IF 0.824) Pub Date : 2019-06-07
    Stefan Ehard, Dieter Rautenbach

    A widely studied model for influence diffusion in socialnetworks are target sets. For a graph G and an integer-valued threshold function τ on its vertex set, a target set or dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the entire vertex set of G. This notion is limited to the binary choice of

    更新日期:2019-06-07
  • Surrogate optimization for p-norms
    Discret. Optim. (IF 0.824) Pub Date : 2019-06-04
    Yasushi Kawase, Kazuhisa Makino

    In this paper, we study the effect of surrogate objective functions in optimizationproblems. We introduce surrogate ratio as a measure of such effect, where the surrogate ratio is the ratio between the optimal values of the original and surrogate objective functions. We prove that the surrogate ratio is at most μ|1∕p−1∕q| when the objective functions are p- and q-norms, and the feasible region is a

    更新日期:2019-06-04
  • Approximating the multiple-depot multiple-terminal Hamiltonian path problem
    Discret. Optim. (IF 0.824) Pub Date : 2019-06-03
    Yichen Yang, Zhaohui Liu

    In this paper, we study a multiple-terminal extension of the classic Hamiltonian path problem where m salesmen are initially located at different depots and finally stopped at different terminals. To the best of our knowledge, only 2-approximation algorithm is available in the literature. For arbitrary m⩾2, we first present a Christofides-like heuristic with a tight approximation ratio of 2−12m+1.

    更新日期:2019-06-03
  • A dual ascent heuristic for obtaining a lower bound of the generalized set partitioning problem with convexity constraints
    Discret. Optim. (IF 0.824) Pub Date : 2019-05-31
    Stefania Pan, Roberto Wolfler Calvo, Mahuna Akplogan, Lucas Létocart, Nora Touati

    In this paper we propose a dual ascent heuristic for solving the linear relaxation of the generalized set partitioning problem with convexity constraints, which often models the master problem of a column generation approach. The generalized set partitioning problem contains at the same time set covering, set packing and set partitioning constraints. The proposed dual ascent heuristic is based on a

    更新日期:2019-05-31
  • A note on submodular function minimization by Chubanov’s LP algorithm
    Discret. Optim. (IF 0.824) Pub Date : 2019-05-03
    Satoru Fujishige

    Recently Dadush et al. (2017) have devised a polynomial submodular function minimization (SFM) algorithm based on their LP algorithm. In the present note we also show a weakly polynomial algorithm for SFM based on the recently developed linear programming feasibility algorithm of Chubanov (2017) to stimulate further research on SFM.

    更新日期:2019-05-03
  • An efficient algorithm for packing cuts and (2,3)-metrics in a planar graph with three holes
    Discret. Optim. (IF 0.824) Pub Date : 2019-04-25
    Alexander V. Karzanov

    We consider a planar graph G in which the edges have nonnegative integer lengths such that the length of every cycle of G is even, and three faces are distinguished, called holes in G. It is known that there exists a packing of cuts and (2,3)-metrics with nonnegative integer weights in G which realizes the distances within each hole. We develop a purely combinatorial strongly polynomial-time algorithm

    更新日期:2019-04-25
  • Combinatorial optimization with interaction costs: Complexity and solvable cases
    Discret. Optim. (IF 0.824) Pub Date : 2019-04-22
    Stefan Lendl, Ante Ćustić, Abraham P. Punnen

    We introduce and study the combinatorial optimization problem with interaction costs (COPIC). COPIC is the problem of finding two combinatorial structures, one from each of two given families, such that the sum of their independent linear costs and the interaction costs between elements of the two selected structures is minimized. COPIC generalizes the quadratic assignment problem and many other well

    更新日期:2019-04-22
  • Global optimization of multilevel electricity market models including network design and graph partitioning
    Discret. Optim. (IF 0.824) Pub Date : 2019-04-15
    Thomas Kleinert, Martin Schmidt

    We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal network expansion and the optimal zonal configuration of zonal pricing electricity markets, which is an extension of the model discussed in Grimm et al. (2019) that does not include a network design problem. The two classical discrete optimization problems of network design

    更新日期:2019-04-15
  • Robust algorithms for total completion time
    Discret. Optim. (IF 0.824) Pub Date : 2019-03-29
    Leah Epstein, Asaf Levin

    We revisit the problem of scheduling or assigning jobs non-preemptively so as to minimize the total completion time on m identical machines and on m uniformly related machines. This problem is polynomially solvable if all jobs are presented at once, even for unrelated machines. An online algorithm receives jobs one by one, such that every job is scheduled before the next job is presented. A robust

    更新日期:2019-03-29
  • Vehicle routing with subtours
    Discret. Optim. (IF 0.824) Pub Date : 2019-03-27
    Stephan Held, Jochen Könemann, Jens Vygen

    When delivering items to a set of destinations, one can save time and cost by passing a subset to a sub-contractor at any point en route. We consider a model where a set of items are initially loaded in one vehicle and should be distributed before a given deadline Δ. In addition to travel time and time for deliveries, we assume that there is a fixed delay for handing over an item from one vehicle to

    更新日期:2019-03-27
  • On the intrinsic volumes of intersections of congruent balls
    Discret. Optim. (IF 0.824) 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
  • Planar multifacility location problems with tree structure and finite dominating sets
    Discret. Optim. (IF 0.824) Pub Date : 2019-03-06
    Andrea Maier, Thomas Ullmert, Horst W. Hamacher

    Multifacility location problems arise in many real world applications. Often, the facilities can only be placed in feasible regions such as development or industrial areas. In this paper we show the existence of a finite dominating set (FDS) for the planar multifacility location problem with polyhedral gauges as distance functions, and polyhedral feasible regions, if the interacting facilities form

    更新日期:2019-03-06
  • Finding the symmetry group of an LP with equality constraints and its application to classifying orthogonal arrays
    Discret. Optim. (IF 0.824) Pub Date : 2019-01-28
    Andrew J. Geyer, Dursun A. Bulutoglu, Kenneth J. Ryan

    For a given linear program (LP) a permutation of its variables that sends feasible points to feasible points and preserves the objective function value of each of its feasible points is a symmetry of the LP. The set of all symmetries of an LP, denoted by GLP, is the symmetry group of the LP. Margot (2010) described a method for computing a subgroup of the symmetry group GLP of an LP. This method computes

    更新日期:2019-01-28
  • Star partitions on graphs
    Discret. Optim. (IF 0.824) Pub Date : 2019-01-25
    G. Andreatta, C. De Francesco, L. De Giovanni, P. Serafini

    Given an undirected graph, a star partition is a partition of the nodes into subsets with at least two nodes so that the subgraph induced by each subset has a spanning star. Star partitions are related to well-known problems concerning domination in graphs and edge covering. We focus on the Constrained Star Partition Problem (CSP) that asks for finding a star partition of given cardinality. The problem

    更新日期:2019-01-25
  • Integrality gaps for colorful matchings
    Discret. Optim. (IF 0.824) Pub Date : 2019-01-11
    Steven Kelk, Georgios Stamoulis

    We study the integrality gap of the natural linear programming relaxation for the Bounded Color Matching (BCM) problem. We provide several families of instances and establish lower bounds on their integrality gaps and we study how the Sherali–Adams “lift-and-project” technique behaves on these instances. We complement these results by showing that if we exclude certain simple sub-structures from our

    更新日期:2019-01-11
  • On the signless Laplacian spectral radius of weighted digraphs
    Discret. Optim. (IF 0.824) Pub Date : 2018-12-21
    Weige Xi, Ligong Wang

    Let G=(V(G),E(G)) be a weighted digraph with vertex set V(G)={v1,v2,…,vn} and arc set E(G), where the arc weights are nonzero nonnegative symmetric matrices. In this paper, we obtain an upper bound on the signless Laplacian spectral radius of a weighted digraph G, and if G is strongly connected, we also characterize the digraphs achieving the upper bound. Moreover, we show that an upper bound of weighted

    更新日期:2018-12-21
  • An integer programming approach to b-coloring
    Discret. Optim. (IF 0.824) Pub Date : 2018-12-17
    Ivo Koch, Javier Marenco

    In the b-coloring problem, we aim to assign colors from a set C to the vertices of a graph G in such a way that adjacent vertices do not receive the same color, and for every c∈C we have a c-colored vertex v in G such that every color in C∖{c} is assigned to at least one of v’s neighbors. It has been shown that b-coloring is NP-complete, so we propose in this article an approach for the problem under

    更新日期:2018-12-17
  • A linear time algorithm for balance vertices on trees
    Discret. Optim. (IF 0.824) Pub Date : 2018-12-10
    Van Huy Pham, Kien Trung Nguyen, Tran Thu Le

    The concept of balance vertices was first investigated by Reid (1999). For the main result “the balance vertices of a tree consist of a single vertex or two adjacent vertices”, Shan and Kang (2004) and Reid and DePalma (2005) improved the length and technique of the proof. In this paper we further discuss the balance vertices on trees in a generalization context. We do not only provide a simple efficient

    更新日期:2018-12-10
  • An algorithmic approach to dual integrality of matching and extensions
    Discret. Optim. (IF 0.824) Pub Date : 2018-11-27
    Yuma Yonebayashi

    Cunningham and Marsh (1978) announced an algorithm to obtain an integral optimum dual solution of weighted matching when every edge weight is integral. Obtaining such a solution is of interest because it reveals min–max properties. This paper provides a faster algorithm to achieve the same purpose. Our method can be extended to b-matching. Although the existence of an integral optimum dual solution

    更新日期:2018-11-27
  • Trader multiflow and box-TDI systems in series–parallel graphs
    Discret. Optim. (IF 0.824) Pub Date : 2018-11-22
    Denis Cornaz, Roland Grappe, Mathieu Lacroix

    Series–parallel graphs are known to be precisely the graphs for which the standard linear systems describing the cut cone, the cycle cone, the T-join polytope, the cut polytope, the multicut polytope and the T-join dominant are TDI. We prove that these systems are actually box-TDI. As a byproduct, our result yields a min–max relation for a new problem: the trader multiflow problem. The latter generalizes

    更新日期:2018-11-22
  • On the NP-hardness of deciding emptiness of the split closure of a rational polytope in the 0,1 hypercube
    Discret. Optim. (IF 0.824) Pub Date : 2018-11-08
    Dabeen Lee

    Split cuts are prominent general-purpose cutting planes in integer programming. The split closure of a rational polyhedron is what is obtained after intersecting the half-spaces defined by all the split cuts for the polyhedron. In this paper, we prove that deciding whether the split closure of a rational polytope is empty is NP-hard, even when the polytope is contained in the unit hypercube. As a direct

    更新日期:2018-11-08
  • Entropy of orthogonal matrices and minimum distance orthostochastic matrices from the uniform van der Waerden matrices
    Discret. Optim. (IF 0.824) Pub Date : 2018-10-29
    K.T. Arasu, Manil T. Mohan

    In this article we formulate an optimization problem of minimizing the distance from the uniform van der Waerden matrices to orthostochastic matrices of different orders. We find a lower bound for the number of stationary points of the minimization problem, which is connected to the number of possible partitions of a natural number. The existence of Hadamard matrices ensures the existence of global

    更新日期:2018-10-29
  • An integral LP relaxation for a drayage problem
    Discret. Optim. (IF 0.824) Pub Date : 2018-10-29
    M. Di Francesco, C. Gentile, S. Schirra, G. Stecca, P. Zuddas

    This paper investigates a drayage problem, where a fleet of trucks must ship container loads from a port to importers and from exporters to the same port, without separating trucks and containers during customer service. We present three formulations for this problem that are valid when each truck carries one container. For the third formulation, we also assume that the arc costs are equal for all

    更新日期:2018-10-29
  • On reachability mixed arborescence packing
    Discret. Optim. (IF 0.824) Pub Date : 2018-10-26
    Tatsuya Matsuoka, Shin-ichi Tanigawa

    As a generalization of Edmonds’ arborescence packing theorem, Kamiyama–Katoh–Takizawa (2009) provided a good characterization of directed graphs that contain arc-disjoint arborescences spanning the set of vertices reachable from each root. Fortier–Király–Léonard–Szigeti–Talon (2018) asked whether the result can be extended to mixed graphs by allowing both directed arcs and undirected edges. In this

    更新日期:2018-10-26
  • An integer optimality condition for column generation on zero–one linear programs
    Discret. Optim. (IF 0.824) Pub Date : 2018-09-27
    Elina Rönnberg, Torbjörn Larsson

    Column generation is a linear programming method that, when combined with appropriate integer programming techniques, has been successfully used for solving huge integer programs. The method alternates between a restricted master problem and a column generation subproblem. The latter step is founded on dual information from the former one; often an optimal dual solution to the linear programming relaxation

    更新日期:2018-09-27
  • The vertex k-cut problem
    Discret. Optim. (IF 0.824) Pub Date : 2018-09-14
    Denis Cornaz, Fabio Furini, Mathieu Lacroix, Enrico Malaguti, A. Ridha Mahjoub, Sébastien Martin

    Given an undirected graph G=(V,E), a vertex k-cut of G is a vertex subset of V the removing of which disconnects the graph in at least k components. Given a graph G and an integer k≥2, the vertex k-cut problem consists in finding a vertex k-cut of G of minimum cardinality. We first prove that the problem is NP-hard for any fixed k≥3. We then present a compact formulation, and an extended formulation

    更新日期:2018-09-14
  • Additive stabilizers for unstable graphs
    Discret. Optim. (IF 0.824) Pub Date : 2018-09-01
    Karthekeyan Chandrasekaran, Corinna Gottschalk, Jochen Könemann, Britta Peis, Daniel Schmand, Andreas Wierz

    A weighted graph is called stable if the maximum weight of an integral matching equals the cost of a minimum-weight fractional vertex cover. We address the following question: how can we modify a given unstable graph in the least intrusive manner in order to achieve stability? Previous works have addressed stabilization through addition or deletion of the smallest possible number of edges/vertices

    更新日期:2018-09-01
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