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8th International Conference on algorithms and Discrete Applied Mathematics

作者： Panda, B. S. Sachin Indian Inst Technol Delhi Dept Math New Delhi 110016 India

ISBN: (纸本)9783030950170;9783030950187

We study several key variants of SMTI - Stable Marriage problem in which the preference lists may contain ties and may be incomplete. A matching is called weakly stable unless there is a man and a woman such that they are currently not matched with each other but if they get matched with each other, then both of them become better off. The COM SMTI problem is to decide whether there exists a complete (in which all men and women are matched) weakly stable matching in an SMTI instance. It is known that the COM SMTI problem is NP-complete. We strengthen this result by proving that this problem remains NP-complete even for the instance SMTI-C, instance where members in each preference list are consecutive with respect to some orderings of the set of men and set of women. On the positive side, we give a polynomial time algorithm for COM SMTI problem for the instance SMTI-STEP, where the preference lists admit step-property, that is, preference list of every man m(i) is the set of all women w(j) such that j <= i for some ordering of men and some ordering of women. Further, DECIDE MAX SMTI (resp. DECIDE_MIN SMTI) is the decision version of MAX SMTI (resp. MIN SMTI), the problem of finding a weakly stable matching of maximum (resp. minimum) cardinality in an SMTI instance. Both DECIDE_MAX SMTI and DECIDE_MIN SMTI problems are known to be NP-complete. We improve these results by showing that DECIDE MAX SMTI and DECIDE_MIN SMTI problems remain NP-complete even for the case where the preference lists admit inclusion ordering and even for the case where the preference lists admit step-property, respectively. Finally, we present a 3/2-approximation algorithm for the MIN SMTI problem with inclusion ordering.

关键词： Stable matching polynomial time algorithm NP-complete Approximation algorithm

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Reconstruction of binary matrices under adjacency constraints

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Electronic Notes in Discrete Mathematics 2005年 20卷 281-297页

作者： Costa, M.-C. Jarray, F. Picouleau, C. CEDRIC CNAM 75003 Paris 292 rue Saint Martin France CEDRIC CNAM 75003 Paris 292 rue Saint Martin France

We consider a generalization of the classical binary matrix reconstruction problem by considering adjacency constraints between the cells: if a given cell is of value 1 then all its neighbors are of value 0. This problem arises especially on statistical physics. We consider several definitions of neighborhood and for each one we give complexity results, necessary and/or sufficient conditions for the existence of a solution and in some cases, polynomial time algorithms. © 2005 Elsevier B.V. All rights reserved.

关键词： adjacency constraint binary matrix reconstruction Discrete tomography network flow NP-complete polynomial time algorithm

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The constrained minimax linear assignment problem

The constrained minimax linear assignment problem

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International Conference on Nonlinear Programming and Variational Inequalities

作者： Charnsethikul, P Kasetsart Univ Dept Ind Engn Operat Res Unit Bangkok Thailand Kasetsart Univ Dept Ind Engn Management Sci Unit Bangkok Thailand

The minimax linear assignment problem with additional linear constraints is studied. An exact polynomial time algorithm is developed, verified and validated in case of a single added constraint. In case of multiple constraints, the problem is more complex and becomes NP-hard. A tree search technique is proposed. Some computational studies are reported.

关键词： combinatorial optimization polynomial time algorithm branch and bound method

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On the Thinness of Trees 7th

On the Thinness of Trees

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7th International Symposium on Combinatorial Optimization (ISCO)

作者： Bonomo-Braberman, Flavia Brandwein, Eric Lucia Gonzalez, Carolina Sansone, Agustin Univ Buenos Aires Fac Ciencias Exactas & Natur Dept Computac Buenos Aires Argentina Univ Buenos Aires Inst Invest Ciencias Computac ICC CONICET Buenos Aires Argentina

ISBN: (纸本)9783031185298;9783031185304

The study of structural graph width parameters like tree-width, clique-width and rank-width has been ongoing during the last five decades, and their algorithmic use has also been increasing [Cygan et al., 2015]. New width parameters continue to be defined, for example, mim-width in 2012, twin-width in 2020, and mixed-thinness, a generalization of thinness, in 2022. The concept of thinness of a graph was introduced in 2007 by Mannino, Oriolo, Ricci and Chandran, and it can be seen as a generalization of interval graphs, which are exactly the graphs with thinness equal to one. This concept is interesting because if a representation of a graph as a k-thin graph is given for a constant value k, then several known NP-complete problems can be solved in polynomial time. Some examples are the maximum weighted independent set problem, solved in the seminal paper by Mannino et al., and the capacitated coloring with fixed number of colors [Bonomo, Mattia and Oriolo, 2011]. In this work we present a constructive O(n log(n))-time algorithm to compute the thinness for any given n-vertex tree, along with a corresponding thin representation. We use intermediate results of this construction to improve known bounds of the thinness of some special families of trees.

关键词： Trees Thinness polynomial time algorithm

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Inventory replenishment planning with a full truckload cost and a full return policy

Inventory replenishment planning with a full truckload cost ...

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16th IFAC Symposium on Information Control Problems in Manufacturing (INCOM)

作者： Farhat, Mlouka Akbalik, Ayse Sauer, Nathalie Hadj-Alouane, Atidel B. Univ Lorraine LGIPM Technopole F-57073 Metz France Univ Lorraine LCOMS Technopole F-57073 Metz France Univ Tunis El Manar OASIS Ecole Natl Ingenieurs Tunis BP 37 Le Belvedere Tunis 1002 Tunisia

This paper addresses the single-item uncapacitated lot sizing problem with batch ordering under the buyback contract between a retailer and a supplier. The form of this type of contract consists in returning all the unused products at the end of every w periods (with w >= 1) to the supplier. This problem is studied with only full batches (OFB), which means that the procurement in each period is restricted to a multiple of a constant batch size, where each demand is satisfied without backlogging and all cost parameters are time-dependent. In this extension, we consider a stepwise discontinuous procurement cost structure due to the fixed cost per batch replenished, incurred by the retailer, in addition to the classical lot sizing costs. Several properties of the optimal solution are proposed to develop an efficient dynamic programming algorithm performed in time complexity O(Tw). (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Lot sizing replenishment planning buyback contract stepwise cost polynomial time algorithm

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On the Recognition of k-Equistable Graphs

On the Recognition of <i>k</i>-Equistable Graphs

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38th International Workshop on Graph-Theoretic Concepts in Computer Science (WG)

作者： Levit, Vadim E. Milanic, Martin Tankus, David Ariel Univ Ctr Samaria Dept Comp Sci & Math IL-40700 Ariel Israel Univ Primorska UP IAM SI-6000 Koper Slovenia Univ Primorska UP FAMNIT SI-6000 Koper Slovenia

ISBN: (纸本)9783642346118;9783642346101

A graph G = (V, E) is called equistable if there exist a positive integer t and a weight function w : V -> N such that S subset of V is a maximal stable set of G if and only if w(S) = t. The function w, if exists, is called an equistable function of G. No combinatorial characterization of equistable graphs is known, and the complexity status of recognizing equistable graphs is open. It is not even known whether recognizing equistable graphs is in NP. Let k be a positive integer. An equistable graph G = (V, E) is said to be k-equistable if it admits an equistable function which is bounded by k. For every constant k, we present a polynomial time algorithm which decides whether an input graph is k-equistable.

关键词： maximal stable set equistable graph polynomial time algorithm

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Network Flow Models for Days Off Scheduling 9th

Network Flow Models for Days Off Scheduling

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9th International Conference on Metaheuristics and Nature Inspired Computing (META)

作者： Tlig, Ghassen Jarray, Fethi Ecole Super Elect Ouest Paris France UTM Univ LIMTIC Lab Tunis Tunisia

ISBN: (纸本)9783031692567;9783031692574

This paper studies the days off scheduling problem when the demand for staffing may differ from day to another and when the total load is fixed in advance for each employee. The scheduling problem is then to assign on-days and days-off to employees with different objectives: (1) exactly met the demand and the offer requirement (2) satisfy as best as possible the requirements. For each one, we propose a polynomial time algorithm based on network flow to construct a feasible scheduling.

关键词： Workforce Scheduling Maximum Flow polynomial time algorithm

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Cost-based solution for optimizing multi-join queries over distributed streaming sensor data

Cost-based solution for optimizing multi-join queries over d...

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International Conference on Collaborative Computing

作者： Gomes, Joseph Choi, Hyeong-Ah George Washington Univ Dept Comp Sci Washington DC 20052 USA

ISBN: (纸本)9781424404285

Sensors are envisioned to be at the center of distributed collaborative computing services involving time-critical decision support. Sensors are small devices with limited communication and computational capabilities that collect data on their neighboring physical world and send the data periodically to server machines. Sensors form a collaborative network with these servers, where the sensors gather information and the servers perform various operations (e.g. filter, aggregate, join etc) on the information streams in real-time according to predefined queries or rules. Sensor data streams are continuous, un-ending and have highly volatile characteristics. As a result, traditional database systems are inappropriate for handling queries for sensor streams, and several stream data management systems have been proposed in the literature. In this paper we focus on a special type of query, namely join queries, which is the most expensive query operator. Here, we address the problem of finding an optimal join tree that maximizes throughput for sliding window based multi-join queries over continuous sensor data streams. We present a polynomial time algorithm Fodp and three variants of Fodp. Our experiments in ARES(1). show that for almost all instances, trees from Fodp and its variants perform close to the optimal trees from our exponential time algorithm OptDP [1], and significantly better than existing XJoin based heuristic algorithms.

关键词： distributed sensors groupware query processing sensor fusion distributed streaming sensor data exponential time algorithm multijoin queries optimal join tree polynomial time algorithm sliding window

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An efficient algorithm for reconstructing binary matrices from horizontal and vertical absorbed projections

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Electronic Notes in Discrete Mathematics 2005年 20卷 347-363页

作者： Frosini, A. Rinaldi, S. Barcucci, E. Kuba, A. Dipartimento di Scienze Matematiche e Informatiche University of Siena Siena Italy Dipartimento di Sistemi e Informatica University of Florence Florence Italy Dept. of Image Proc. and Computer Graphics Univ. of Szeged Szeged Hungary

This paper studies the classical tomographical problem of the reconstruction of a binary matrix from projections in presence of absorption. In particular, we consider two projections along the horizontal and vertical directions and the mathematically interesting case of the absorption coefficient β₀ = frac(1 + sqrt(5), 2). After proving some theoretical results on the switching components, we furnish a fast algorithm for solving the reconstruction problem from the horizontal and vertical absorbed projections. As a significative remark, we obtain also the solution of the related uniqueness problem. © 2005 Elsevier B.V. All rights reserved.

关键词： absorbed projections Discrete tomography polynomial time algorithm reconstruction problem

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Reconstruction of Interval Graphs

Reconstruction of Interval Graphs

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15th Annual International Conference on Computing and Combinatorics (COCOON 2009)

作者： Kiyomi, Masashi Saitoh, Toshiki Uehara, Ryuhei JAIST Sch Informat Sci Nomi Ishikawa 9231292 Japan

ISBN: (纸本)9783642028816

The graph reconstruction conjecture is a long-standing open problem in graph theory. There are many algorithmic studies related it besides mathematical studies, such as DECK CHECKING, LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING. We study these algorithmic problems limiting the graph class to interval graphs. Since we can solve GRAPH ISOMORPHISM for interval graphs in polynomial time, DECK CHECKING for interval graphs is easily done in polynomial time. Since the number of interval graphs that can be obtained from an interval graph by adding a vertex and edges incident to it can be exponentially large, developing polynomial time algorithms for LEGITIMATE DECK, PREIMACE CONSTRUCTION, and PREIMAGE COUNTING on interval graphs is not trivial. We present that these three problems are solvable in polynomial time on interval graphs.

关键词： the graph reconstruction conjecture interval graphs polynomial time algorithm

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