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On Pareto optimal balanced exchanges Discret. Optim. (IF 1.1) Pub Date : 2024-03-05 Pavlos Eirinakis, Ioannis Mourtos, Michalis Samaris
We investigate a market without money in which every agent offers indivisible goods in multiple copies, in exchange for goods of other agents. The exchange must be balanced in the sense that each agent should receive a quantity of good(s) equal to the one she transfers to others. We describe the market in graph-theoretic terms hence we use the notion of circulations to describe a balanced exchange
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Circuits in extended formulations Discret. Optim. (IF 1.1) Pub Date : 2024-02-09 Steffen Borgwardt, Matthias Brugger
Circuits and extended formulations are classical concepts in linear programming theory. The circuits of a polyhedron are the elementary difference vectors between feasible points and include all edge directions. We study the connection between the circuits of a polyhedron and those of an extended formulation of , i.e., a description of a polyhedron that linearly projects onto . It is well known that
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When greedy gives optimal: A unified approach Discret. Optim. (IF 1.1) Pub Date : 2024-01-25 Dmitry Rybin
We present necessary and sufficient conditions when a certain greedy object selection algorithm gives optimal results. Our approach covers known results for the Unbounded Knapsack Problem and Change Making Problem and gives new theoretical results for a variety of packing problems. We also provide connections between packing problems and certain bidirectional capacity installation problems on networks
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Parametric matroid interdiction Discret. Optim. (IF 1.1) Pub Date : 2024-01-25 Nils Hausbrandt, Oliver Bachtler, Stefan Ruzika, Luca E. Schäfer
We introduce the parametric matroid one-interdiction problem. Given a matroid, each element of its ground set is associated with a weight that depends linearly on a real parameter from a given parameter interval. The goal is to find, for each parameter value, one element that, when being removed, maximizes the weight of a minimum weight basis. The complexity of this problem can be measured by the number
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On polytopes with linear rank with respect to generalizations of the split closure Discret. Optim. (IF 1.1) Pub Date : 2024-01-18 Sanjeeb Dash, Yatharth Dubey
In this paper we study the rank of polytopes contained in the 0-1 cube with respect to t-branch split cuts and t-dimensional lattice cuts for a fixed positive integer t. These inequalities are the same as split cuts when t=1 and generalize split cuts when t>1. For polytopes contained in the n-dimensional 0-1 cube, the work of Balas implies that the split rank can be at most n, and this bound is tight
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Tighter bounds on the minimum broadcast time Discret. Optim. (IF 1.1) Pub Date : 2024-01-13 Dag Haugland
Given a connected graph and a subset of its vertices referred to as the sources, the minimum broadcast time problem asks for the shortest time necessary for communicating a message from the sources to all other vertices in the graph. Information exchange is possible only between neighbors, and each vertex can transmit the message to at most one neighbor at a time. Since early works on complexity theory
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Characterizing linearizable QAPs by the level-1 reformulation-linearization technique Discret. Optim. (IF 1.1) Pub Date : 2023-11-21 Lucas Waddell, Warren Adams
The quadratic assignment problem (QAP) is an extremely challenging NP-hard combinatorial optimization program. Due to its difficulty, a research emphasis has been to identify special cases that are polynomially solvable. Included within this emphasis are instances which are linearizable; that is, which can be rewritten as a linear assignment problem having the property that the objective function value
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Packing mixed hyperarborescences Discret. Optim. (IF 1.1) Pub Date : 2023-11-14 Zoltán Szigeti
The aim of this paper is twofold. We first provide a new orientation theorem which gives a natural and simple proof of a result of Gao and Yang (2021) on matroid-reachability-based packing of mixed arborescences in mixed graphs by reducing it to the corresponding theorem of Király (2016) on directed graphs. Moreover, we extend another result of Gao and Yang (2021) by providing a new theorem on mixed
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Hard problems on box-totally dual integral polyhedra Discret. Optim. (IF 1.1) Pub Date : 2023-11-08 Patrick Chervet, Roland Grappe, Mathieu Lacroix, Francesco Pisanu, Roberto Wolfler Calvo
In this paper, we study the complexity of some fundamental questions regarding box-totally dual integral (box-TDI) polyhedra. First, although box-TDI polyhedra have strong integrality properties, we prove that Integer Programming over box-TDI polyhedra is NP-complete, that is, finding an integer point optimizing a linear function over a box-TDI polyhedron is hard. Second, we complement the result of
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The maximum number of short paths in a Halin graph Discret. Optim. (IF 1.1) Pub Date : 2023-11-03 Shunhai He, Huiqing Liu
A Halin graph G is a plane graph consisting of a plane embedding of a tree T of order at least 4 containing no vertex of degree 2, and of a cycle C connecting all leaves of T. Let fh(n,G) be the maximum number of copies of G in a Halin graph on n vertices. In this paper, we give exact values of fh(n,G) when G is a path on k vertices for 2≤k≤5. Moreover, we develop a new graph transformation preserving
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Optimal length cutting plane refutations of integer programs Discret. Optim. (IF 1.1) Pub Date : 2023-10-14 K. Subramani, Piotr Wojciechowski
In this paper, we discuss the computational complexities of determining optimal length refutations of infeasible integer programs (IPs). We focus on three different types of refutations, namely read-once refutations, tree-like refutations, and dag-like refutations. For each refutation type, we are interested in finding the length of the shortest possible refutation of that type. In the case of this
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On the general Z-type index of connected graphs Discret. Optim. (IF 1.1) Pub Date : 2023-10-09 Chaohui Chen, Wenshui Lin
Let G=(V,E) be a connected graph, and d(u) the degree of vertex u∈V. We define the general Z-type index of G as Zα,β(G)=∑uv∈E[d(u)+d(v)−β]α, where α and β are two real numbers. This generalizes several famous topological indices, such as the first and second Zagreb indices, the general sum-connectivity index, the reformulated first Zagreb index, and the general Platt index, which have successful applications
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On cut polytopes and graph minors Discret. Optim. (IF 1.1) Pub Date : 2023-10-10 Konstantinos Kaparis, Adam N. Letchford, Ioannis Mourtos
The max-cut problem is a fundamental and much-studied NP-hard combinatorial optimisation problem, with a wide range of applications. Several authors have shown that the max-cut problem can be solved in polynomial time if the underlying graph is free of certain minors. We give a polyhedral counterpart of these results. In particular, we show that, if a family of valid inequalities for the cut polytope
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The k-aggregation closure for covering sets Discret. Optim. (IF 1.1) Pub Date : 2023-09-26 Haoran Zhu
In this paper, we will answer a more general version of one of the questions proposed by Bodur et al. (2017). Specifically, we show that the k-aggregation closure of a covering set is a polyhedron.
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Convexifying multilinear sets with cardinality constraints: Structural properties, nested case and extensions Discret. Optim. (IF 1.1) Pub Date : 2023-09-16 Rui Chen, Sanjeeb Dash, Oktay Günlük
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained version of it with upper and lower bounds on the number of nonzero variables. We call the set of solutions of the standard linearization of this problem a multilinear
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More on online weighted edge coloring Discret. Optim. (IF 1.1) Pub Date : 2023-09-13 Leah Epstein
We revisit online weighted edge coloring. In this problem, weighted edges of a graph are presented one by one, to be colored with positive integers. It is required that for every vertex, all its edges of every common color will have a total weight not exceeding 1. We provide an improved upper bound on the performance of a greedy algorithm First Fit for the case of arbitrary weights, and for the case
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Constructing extremal triangle-free graphs using integer programming Discret. Optim. (IF 1.1) Pub Date : 2023-09-05 Ali Erdem Banak, Tınaz Ekim, Z. Caner Taşkın
The maximum number of edges in a graph with matching number m and maximum degree d has been determined in Chvátal and Hanson (1976) and Balachandran and Khare (2009), where some extremal graphs have also been provided. Then, a new question has emerged: how the maximum edge count is affected by forbidding some subgraphs occurring in these extremal graphs? In Ahanjideh et al. (2022), the problem is solved
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Principled deep neural network training through linear programming Discret. Optim. (IF 1.1) Pub Date : 2023-08-07 Daniel Bienstock, Gonzalo Muñoz, Sebastian Pokutta
Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become more evident and multiple works in recent years have focused on this task. In this work, using a unified framework, we show that there exists a polyhedron that simultaneously encodes, in
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Secretary and online matching problems with machine learned advice Discret. Optim. (IF 1.1) Pub Date : 2023-06-09 Antonios Antoniadis, Themis Gouleakis, Pieter Kleer, Pavel Kolev
The classic analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. In contrast, machine learning approaches shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three
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Graphs with equal Grundy domination and independence number Discret. Optim. (IF 1.1) Pub Date : 2023-05-29 Gábor Bacsó, Boštjan Brešar, Kirsti Kuenzel, Douglas F. Rall
The Grundy domination number, γgr(G), of a graph G is the maximum length of a sequence (v1,v2,…,vk) of vertices in G such that for every i∈{2,…,k}, the closed neighborhood N[vi] contains a vertex that does not belong to any closed neighborhood N[vj], where j
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The polytope of binary sequences with bounded variation Discret. Optim. (IF 1.1) Pub Date : 2023-05-11 Christoph Buchheim, Maja Hügging
We investigate the problem of optimizing a linear objective function over the set of all binary vectors of length n with bounded variation, where the latter is defined as the number of pairs of consecutive entries with different value. This problem arises naturally in many applications, e.g., in unit commitment problems or when discretizing binary optimal control problems subject to a bounded total
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EPTAS for load balancing problem on parallel machines with a non-renewable resource Discret. Optim. (IF 1.1) Pub Date : 2023-05-06 G. Jaykrishnan, Asaf Levin
The problem considered is the non-preemptive scheduling of independent jobs that consume a resource (which is non-renewable and replenished regularly) on parallel uniformly related machines. The input defines the speed of machines, size of jobs, the quantity of the resource required by the jobs, the replenished quantities, and replenishment dates of the resource. Every job can start processing only
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Minimum gradation in greyscales of graphs Discret. Optim. (IF 1.1) Pub Date : 2023-04-21 Natalia de Castro, María A. Garrido-Vizuete, Rafael Robles, María Trinidad Villar-Liñán
In this paper we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours are ordered in lexicographical decreasing ordering and give rise to a new element of the graph: the gradation vector
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The complexity of 2-vertex-connected orientation in mixed graphs Discret. Optim. (IF 1.1) Pub Date : 2023-04-21 Florian Hörsch, Zoltán Szigeti
We consider two possible extensions of a theorem of Thomassen characterizing the graphs admitting a 2-vertex-connected orientation. First, we show that the problem of deciding whether a mixed graph has a 2-vertex-connected orientation is NP-hard. This answers a question of Bang-Jensen, Huang and Zhu. For the second part, we call a directed graph D=(V,A) 2T-connected for some T⊆V if D is 2-arc-connected
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On the Rényi–Ulam game with restricted size queries Discret. Optim. (IF 1.1) Pub Date : 2023-04-01 Ádám X. Fraknói, Dávid Á. Márton, Dániel G. Simon, Dániel A. Lenger
We investigate the following version of the well-known Rényi–Ulam game. Two players – the Questioner and the Responder – play against each other. The Responder thinks of a number from the set {1,…,n}, and the Questioner has to find this number. To do this, he can ask whether a chosen set of at most k elements contains the thought number. The Responder answers with YES or NO immediately, but during
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Approximating single- and multi-objective nonlinear sum and product knapsack problems Discret. Optim. (IF 1.1) Pub Date : 2023-03-09 Jan Boeckmann, Clemens Thielen, Ulrich Pferschy
We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint
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Maximizing the Mostar index for bipartite graphs and split graphs Discret. Optim. (IF 1.1) Pub Date : 2023-02-25 Štefko Miklavič, Johannes Pardey, Dieter Rautenbach, Florian Werner
Došlić et al. defined the Mostar index of a graph G as ∑uv∈E(G)|nG(u,v)−nG(v,u)|, where, for an edge uv of G, the term nG(u,v) denotes the number of vertices of G that have a smaller distance in G to u than to v. Contributing to conjectures posed by Došlić et al., we show that the Mostar index of bipartite graphs of order n is at most 318n3, and that the Mostar index of split graphs of order n is at
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Reachability in choice networks Discret. Optim. (IF 1.1) Pub Date : 2023-02-21 Piotr Wojciechowski, K. Subramani, Alvaro Velasquez
In this paper, we investigate the problem of determining s−t reachability in choice networks. In the traditional s−t reachability problem, we are given a weighted network tuple G=〈V,E,c,s,t〉, with the goal of checking if there exists a path from s to t in G. In an optional choice network, we are given a choice set S⊆E×E, in addition to the network tuple G. In the s−t reachability problem in choice
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A polyhedral study of lifted multicuts Discret. Optim. (IF 1.1) Pub Date : 2023-02-08 Bjoern Andres, Silvia Di Gregorio, Jannik Irmai, Jan-Hendrik Lange
Fundamental to many applications in data analysis are the decompositions of a graph, i.e. partitions of the node set into component-inducing subsets. One way of encoding decompositions is by multicuts, the subsets of those edges that straddle distinct components. Recently, a lifting of multicuts from a graph G=(V,E) to an augmented graph Ĝ=(V,E∪F) has been proposed in the field of image analysis,
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The p-center problem under locational uncertainty of demand points Discret. Optim. (IF 1.1) Pub Date : 2023-01-25 Homa Ataei, Mansoor Davoodi
The p-center problem is finding the location of p facilities among a set of n demand points such that the maximum distance between any demand point and its nearest facility is minimized. In this paper, we study this problem in the context of uncertainty, that is, the location of the demand points may change in a region like a disk or a segment, or belong to a finite set of points. We introduce Max-p-center
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CHAMP: A multipass algorithm for Max Sat based on saver variables Discret. Optim. (IF 1.1) Pub Date : 2023-01-23 Daniel Berend, Shahar Golan, Yochai Twitto
In this paper, we introduce the concept of saver variables in Max Sat and demonstrate their contribution to the performance of solvers for this problem. We present two types of saver variables: high-rank savers and consensual savers. We show how to incorporate them in various ways into an iterated algorithm, CHAMP, for Max Sat. We conduct an extensive empirical evaluation on two collections of instances
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The Aα-spectral radius of nonregular graphs (digraphs) and maximum degree (outdegree) Discret. Optim. (IF 1.1) Pub Date : 2022-12-24 Qixuan Yuan, Ruifang Liu, Jinjiang Yuan
For 0≤α<1, let Aα(G)=αD(G)+(1−α)A(G) be the Aα-matrix of G, where D(G) is the diagonal degree matrix of G and A(G) is the adjacency matrix of G Let λα(G) denote the Aα-spectral radius of a graph G. Let G be a k-connected nonregular graph with n vertices, m edges, maximum degree Δ and minimum degree δ. In this paper, we show that Δ−λα(G)>(1−α)(nΔ−2m)k2(nΔ−2m)(n−1)2−(Δ−k+1)(n−k−1)+(1−α)nk2,which extends
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Constant factor approximation for tracking paths and fault tolerant feedback vertex set Discret. Optim. (IF 1.1) Pub Date : 2022-12-19 Václav Blažej, Pratibha Choudhary, Dušan Knop, Jan Matyáš Křišťan, Ondřej Suchý, Tomáš Valla
Consider a vertex-weighted graph G with a source s and a target t. Tracking Paths requires finding a minimum weight set of vertices (trackers) such that the sequence of trackers in each path from s to t is unique. In this work, we derive a factor 6-approximation algorithm for Tracking Paths in weighted graphs and a factor 4-approximation algorithm if the input is unweighted. This is the first constant
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An improved greedy algorithm for stochastic online scheduling on unrelated machines Discret. Optim. (IF 1.1) Pub Date : 2022-12-16 Sven Jäger
Most practical scheduling applications involve some uncertainty about the arriving times and lengths of the jobs. Stochastic online scheduling is a well-established model capturing this. Here the arrivals occur online, while the processing times are random. For this model, Gupta, Moseley, Uetz, and Xie recently devised an efficient policy for non-preemptive scheduling on unrelated machines with the
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Fractional Decomposition Tree Algorithm: A tool for studying the integrality gap of Integer Programs Discret. Optim. (IF 1.1) Pub Date : 2022-12-05 Robert Carr, Arash Haddadan, Cynthia A. Phillips
We present a new algorithm, Fractional Decomposition Tree (FDT), for finding a feasible solution for an integer program (IP) where all variables are binary. FDT runs in polynomial time and is guaranteed to find a feasible integer solution provided the integrality gap of an instance’s polyhedron, independent of objective function, is bounded. The algorithm gives a construction for Carr and Vempala’s
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Packing strong subgraph in digraphs Discret. Optim. (IF 1.1) Pub Date : 2022-11-04 Yuefang Sun, Gregory Gutin, Xiaoyan Zhang
In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint strong subgraph packing problem and arc-disjoint strong subgraph packing problem. These problems can be viewed as generalizations of the famous Steiner tree packing problem and are closely related to the strong arc decomposition problem. We first prove the NP-completeness for the internally
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The (d−2)-leaky forcing number of Qd and ℓ-leaky forcing number of GP(n,1) Discret. Optim. (IF 1.1) Pub Date : 2022-10-22 Rebekah Herrman
Leaky-forcing is a recently introduced variant of zero forcing that has been studied for families of graphs including paths, cycles, wheels, grids, and trees. In this paper, we extend previous results on the leaky forcing number of the d-dimensional hypercube, Qd, to show that the (d−2)-leaky forcing number of Qd is 2d−1. We also examine a question about the relationship between the size of a minimum ℓ-leaky-forcing
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Block-structured integer programming: Can we parameterize without the largest coefficient? Discret. Optim. (IF 1.1) Pub Date : 2022-10-12 Hua Chen, Lin Chen, Guochuan Zhang
We consider 4-block n-fold integer programming, which can be written as max{w⋅x:Hx=b,l≤x≤u,x∈ZN}, where the constraint matrix H is composed of small matrices A,B,C,D such that the first row of H is (C,D,D,…,D), the first column of H is (C,B,B,…,B), the main diagonal of H is (C,A,A,…,A), and all the other entries are 0. There are n copies of D, B, and A. The special case where B=C=0 is known as n-fold
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A polyhedral study for the cubic formulation of the unconstrained traveling tournament problem Discret. Optim. (IF 1.1) Pub Date : 2022-10-09 Marije R. Siemann, Matthias Walter
We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In this paper we carry out a polyhedral study for the cubic integer programming formulation by establishing the dimension of the integer hull as well as of faces induced
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Cardinality constrained connected balanced partitions of trees under different criteria Discret. Optim. (IF 1.1) Pub Date : 2022-09-30 Roberto Cordone, Davide Franchi, Andrea Scozzari
In this paper we study the problem of partitioning a tree with n weighted vertices into p connected components. For each component, we measure its gap, that is, the difference between the maximum and the minimum weight of its vertices, with the aim of minimizing the sum of such differences. We present an O(n3p2) time and O(n3p) space algorithm for this problem. Then, we generalize it, requiring a minimum
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Parameterized algorithms for generalizations of Directed Feedback Vertex Set Discret. Optim. (IF 1.1) Pub Date : 2022-09-13 Alexander Göke, Dániel Marx, Matthias Mnich
The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph G and seeks a smallest vertex set S that hits all cycles in G. This is one of Karp’s 21 NP-complete problems. Resolving the parameterized complexity status of DFVS was a long-standing open problem until Chen et al. (2008) showed its fixed-parameter tractability via a 4kk!nO(1)-time algorithm, where k=|S|. Here we show fixed-parameter
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Stable allocations and partially ordered sets Discret. Optim. (IF 1.1) Pub Date : 2022-08-06 Ioannis Mourtos, Michalis Samaris
We provide a linear description of the unconstrained stable allocations problem by proving that the corresponding polytope is affinely congruent to the order polytope of a partially ordered set. The same holds for stable matchings hence simplifying the derivation of known polyhedral results. We also show that this congruence no longer holds for the constrained version of stable allocations. As side
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On the analysis of optimization problems in arc-dependent networks Discret. Optim. (IF 1.1) Pub Date : 2022-07-14 P. Wojciechowski, M. Williamson, K. Subramani
This paper is concerned with the design and analysis of algorithms for optimization problems in arc-dependent networks. A network is said to be arc-dependent if the cost of an arc a depends upon the arc taken to enter a. These networks are fundamentally different from traditional networks in which the cost associated with an arc is a fixed constant and part of the input. We first study the arc-dependent
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Finding the dimension of a non-empty orthogonal array polytope Discret. Optim. (IF 1.1) Pub Date : 2022-06-25 Dursun A. Bulutoglu
By using representation theory, we reduce the size of the set of possible values for the dimension of the convex hull of all feasible points of an orthogonal array (OA) defining integer linear description (ILD). Our results address the conjecture that if this polytope is non-empty, then it is full-dimensional within the affine space where all the feasible points of the ILD’s linear description (LD)
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On the length of L-Grundy sequences Discret. Optim. (IF 1.1) Pub Date : 2022-06-24 Rebekah Herrman, Stephen G.Z. Smith
An L-sequence of a graph G is a sequence of distinct vertices S=(v1,…,vk) such that N[vi]∖∪j=1i−1N(vj)≠0̸. The length of a longest L-sequence is called the L-Grundy domination number, denoted γgrL(G). In this paper, we prove γgrL(G)≤n(G)−δ(G)+1, which was conjectured by Brešar, Gologranc, Henning, and Kos. We also prove some initial results about characteristics of n-vertex graphs satisfying γgrL(G)=n
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The Arc-Item-Load and Related Formulations for the Cumulative Vehicle Routing Problem Discret. Optim. (IF 1.1) Pub Date : 2022-06-07 Mauro Henrique Mulati, Ricardo Fukasawa, Flávio Keidi Miyazawa
The Capacitated Vehicle Routing Problem (CVRP) consists of finding the cheapest way to serve a set of customers with a fleet of vehicles of a given capacity. While serving a particular customer, each vehicle picks up its demand and carries its weight throughout the rest of its route. While costs in the classical CVRP are measured in terms of a given arc distance, the Cumulative Vehicle Routing Problem
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LP-based approximation for uniform capacitated facility location problem Discret. Optim. (IF 1.1) Pub Date : 2022-06-02 Sapna Grover, Neelima Gupta, Samir Khuller
In this paper, we study uniform hard capacitated facility location problem. The standard LP for the problem is known to have an unbounded integrality gap. We present constant factor approximation by rounding a solution to the standard LP with a slight (1+ε) violation in the capacities. Our result shows that the standard LP is not too bad. Our algorithm is simple and more efficient as compared to the
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On packing time-respecting arborescences Discret. Optim. (IF 1.1) Pub Date : 2022-04-28 Romain Chapoullié, Zoltán Szigeti
We present a slight generalization of the result of Kamiyama and Kawase (2015) on packing time-respecting arborescences in acyclic pre-flow temporal networks. Our main contribution is to provide the first results on packing time-respecting arborescences in non-acyclic temporal networks. As negative results, we prove the NP-completeness of the decision problem of the existence of 2 arc-disjoint spanning
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A theoretical justification of the set covering greedy heuristic of Caprara et al. Discret. Optim. (IF 1.1) Pub Date : 2022-03-28 Torbjörn Larsson, Nils-Hassan Quttineh
Large scale set covering problems have often been approached by constructive greedy heuristics, and much research has been devoted to the design and evaluation of various greedy criteria for such heuristics. A criterion proposed by Caprara et al. (1999) is based on reduced costs with respect to the yet unfulfilled constraints, and the resulting greedy heuristic is reported to be superior to those based
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Two-agent bounded parallel-batching scheduling for minimizing maximum cost and makespan Discret. Optim. (IF 1.1) Pub Date : 2022-03-19 Cheng He, Jing Wu, Hao Lin
This paper considers the bounded parallel-batching scheduling with two agents to minimize maximum cost of agent A and makespan of agent B simultaneously, in which all jobs of agent A have equal processing time, the jobs from different agents can be processed in a common batch and the cost function of each agent is only determined by its own jobs. In the paper, we present a polynomial-time algorithm
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GO-MOCE: Greedy Order Method of Conditional Expectations for Max Sat Discret. Optim. (IF 1.1) Pub Date : 2022-02-07 Daniel Berend, Shahar Golan, Yochai Twitto
In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson’s Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined
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Node-based valid inequalities for the optimal transmission switching problem Discret. Optim. (IF 1.1) Pub Date : 2022-02-05 Santanu S. Dey, Burak Kocuk, Nicole Redder
The benefits of transmission line switching are well-known in terms of reducing operational cost and improving system reliability of power systems. However, finding the optimal power network configuration is a challenging task due to the combinatorial nature of the underlying optimization problem. In this work, we identify a certain “node-based” set that appears as substructure of the optimal transmission
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An improved zig zag approach for competitive group testing Discret. Optim. (IF 1.1) Pub Date : 2022-01-25 Jun Wu, Yongxi Cheng, Ding-Zhu Du
In many fault detection problems, we want to identify defective items from a set of n items using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells whether the subset contains at least one defective item or not. In practice, the number d of defective items is often unknown in advance. In this paper, we improve the previously best algorithm
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A column generation approach to the discrete barycenter problem Discret. Optim. (IF 1.1) Pub Date : 2021-11-20 Steffen Borgwardt, Stephan Patterson
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be extremely large. For worst-case input, a best known linear programming formulation is exponential in the number of variables, but has a low number of constraints, making
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Mathematical formulations and solution methods for the uncapacitated r-allocation p-hub maximal covering problem Discret. Optim. (IF 1.1) Pub Date : 2021-11-13 Olivera Stančić, Zorica Stanimirović, Raca Todosijević, Stefan Mišković
This paper considers the uncapacitated r-allocation p-hub maximal covering problem (UrApHMCP), which represents a generalization of the well-known p-hub maximal covering problem, as it allows each non-hub node to send and receive flow via at most r hubs, r≤p. Two coverage criteria are considered in UrApHMCP — binary and, for the first time in the literature, partial coverage. Novel mathematical formulations
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Exact values of defective Ramsey numbers in graph classes Discret. Optim. (IF 1.1) Pub Date : 2021-11-03 Yunus Emre Demirci, Tınaz Ekim, John Gimbel, Mehmet Akif Yıldız
Given a graph G, a k-sparse j-set is a set of j vertices inducing a subgraph with maximum degree at most k. A k-dense i-set is a set of i vertices that is k-sparse in the complement of G. As a generalization of Ramsey numbers, the k-defective Ramsey number RkG(i,j) for the graph class G is defined as the smallest natural number n such that all graphs on n vertices in the class G have either a k-dense