We are interested in the reconstruction of a domino tiling of a rectangle from its two orthogonal projections. We give polynomialalgorithms for some subproblems when all the dominoes are of the same type and prove NP...
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We are interested in the reconstruction of a domino tiling of a rectangle from its two orthogonal projections. We give polynomialalgorithms for some subproblems when all the dominoes are of the same type and prove NP-completeness results when there are three types of dominoes. When two types of dominoes are allowed. we give a polynomial-time transformation from a well-known open problem. (C) 2001 Elsevier Science B.V. All rights reserved.
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in...
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In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomialtime. Using mainly tools from discrete geometry, we show that some sparsity conditions on the original data matrix allow us to solve the problem in polynomialtime.
Given an undirected graph and pairs of terminals the RESTRICTED VERTEX MULTICUT problem asks for a minimum set of nonterminal vertices whose removal disconnects each pair of terminals. The problem is known to be NP-co...
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Given an undirected graph and pairs of terminals the RESTRICTED VERTEX MULTICUT problem asks for a minimum set of nonterminal vertices whose removal disconnects each pair of terminals. The problem is known to be NP-complete for trees and polynomial-time solvable for interval graphs. In this paper we give a polynomial-time algorithm for the problem on permutation graphs. Furthermore we show that the problem remains NP-complete on split graphs whereas it becomes polynomial-time solvable for the class of co-bipartite graphs. (C) 2012 Elsevier B.V. All rights reserved.
This paper considers a multi-objective aircraft recovery problem for airline disruption. An integer programming formulation is first established based on connection network with three conflicting objectives, where the...
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This paper considers a multi-objective aircraft recovery problem for airline disruption. An integer programming formulation is first established based on connection network with three conflicting objectives, where the first objective minimizes the total deviation from original flight schedules, the second objective minimizes the maximal flight delay time, and the third objective minimizes the number of aircraft actually attended in swapping. Optimal analysis is provided for a small scale aircraft recovery problem with the last two objectives and then one polynomialtimealgorithm for aircraft recovery problem after the disruption to multi-aircraft in a fleet at an airport. One heuristic combined epsilon-constraints method and neighborhood search algorithm is designed for large scale disruption recovery problem. The results obtained from computational experiment illustrate effectiveness and efficiency of the heuristic. The outcome of this research could provide theoretical and practical supports for airlines to reduce flight delays. (C) 2017 Elsevier Ltd. All rights reserved.
The x-and-y-axes travelling salesman problem forms a special case of the Euclidean TSP, where all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system of the Euclidean plane. By caref...
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The x-and-y-axes travelling salesman problem forms a special case of the Euclidean TSP, where all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system of the Euclidean plane. By carefully analyzing the underlying combinatorial and geometric structures, we show that this problem can be solved in polynomialtime. The running time of the resulting algorithm is quadratic in the number of cities. (C) 2012 Elsevier By. All rights reserved.
In this paper, we investigate the Colourability problem for dually chordal graphs and some of its generalisations. We show that the problem remains NP-complete if limited to four colours. For the case of three colours...
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In this paper, we investigate the Colourability problem for dually chordal graphs and some of its generalisations. We show that the problem remains NP-complete if limited to four colours. For the case of three colours, we present a simple linear timealgorithm for dismantlable graphs (which include dually chordal graphs) and present an O(n(3)m) timealgorithm for graphs with tree-breadth 1. Additionally, we show that a dually chordal graph is 3-colourable if and only if it is perfect and has no clique of size four. (C) 2017 Elsevier B.V. All rights reserved.
A k-extremal point set is a point set on the boundary of a k-sided rectilinear convex hull. Given a k-extremal point set of size n, we present an algorithm that computes a rectilinear Steiner minimal tree in time O(k4...
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A k-extremal point set is a point set on the boundary of a k-sided rectilinear convex hull. Given a k-extremal point set of size n, we present an algorithm that computes a rectilinear Steiner minimal tree in time O(k4n). For constant k, this algorithm runs in O(n) time and is asymptotically optimal and, for arbitrary k, the algorithm is the fastest known for this problem,
In this paper, we investigate a joint multitasking scheduling and common due date assignment problem on a single machine, for which examples can be found in product delivery process in logistics. Multitasking allows t...
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In this paper, we investigate a joint multitasking scheduling and common due date assignment problem on a single machine, for which examples can be found in product delivery process in logistics. Multitasking allows the machine to perform multiple tasks. The multitasking phenomenon has been observed in various practical domains, including manufacturing and administration. In multitasking settings, each waiting job interrupts a currently in-processing job, causing an interruption time and a switching time. In common due date assignment problems, the objective is to determine the optimal value of this due date with the purpose of minimising a total penalty function, which is associated with service quality. For the problem with general interruption functions, analytical properties are obtained to reduce the search space of the optimal solutions. For the cases with linear interruption functions, we develop a polynomial-time algorithm. Numerical experiments have been conducted to validate the efficiency of our proposed algorithm. Computational results also demonstrate an interesting phenomenon that in some cases, the optimal solutions under multitasking are superior to the counterparts without multitasking. Besides, we also devise a mixed integer programme for the cases with linear interruption function.
The Min-Min problem of finding a disjoint-path pair with the length of the shorter path minimized is known to be NP-hard and admits no K-approximation for any K > 1 in the general case (Xu et al. in IEEE/ACM Trans....
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The Min-Min problem of finding a disjoint-path pair with the length of the shorter path minimized is known to be NP-hard and admits no K-approximation for any K > 1 in the general case (Xu et al. in IEEE/ACM Trans. Netw. 14:147-158, 2006). In this paper, we first show that Bhatia et al.'s NP-hardness proof (Bhatia et al. in J. Comb. Optim. 12:83-96, 2006), a claim of correction to Xu et al.'s proof (Xu et al. in IEEE/ACM Trans. Netw. 14:147-158, 2006), for the edge-disjoint Min-Min problem in the general undirected graphs is incorrect by giving a counter example that is an unsatisfiable 3SAT instance but classified as a satisfiable 3SAT instance in the proof of Bhatia et al. (J. Comb. Optim. 12:83-96, 2006). We then gave a correct proof of NP-hardness of this problem in undirected graphs. Finally we give a polynomial-time algorithm for the vertex disjoint Min-Min problem in planar graphs by showing that the vertex disjoint Min-Min problem is polynomially solvable in st-planar graph G=(V,E) whose corresponding auxiliary graph G(V,Ea(a){e(st)}) can be embedded into a plane, and a planar graph can be decomposed into several st-planar graphs whose Min-Min paths collectively contain a Min-Min disjoint-path pair between s and t in the original graph G. To the best of our knowledge, these are the first polynomialalgorithms for the Min-Min problems in planar graphs.
We provide a novel heuristic approach to solve a class of multivariate set partitioning problems in which each item is characterized by three attribute values. The scheme first identifies a series of orderings of the ...
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We provide a novel heuristic approach to solve a class of multivariate set partitioning problems in which each item is characterized by three attribute values. The scheme first identifies a series of orderings of the items and then solves a corresponding sequence of shortest path problems. We provide theoretical findings on the structure of an optimal solution that motivate the design of the proposed heuristic scheme. The proposed algorithm runs in polynomial-time and is independent of the number of groups in the partition, making it more efficient than existing algorithms. To measure the performance of our solutions, we construct bounds for special instances which allow us to provide optimality gaps. We conduct an extensive numerical experiment in which we solve a large number of problem instances and show that our proposed approach converges to the global optimal solution in the vast majority of cases and in the case it does not, it yields very low optimality gaps. We demonstrate our findings with an application in the context of classifying a large heterogeneous population as positive or negative for multiple binary attributes as efficiently as possible. We conduct a case study on the screening of three of the most prevalent sexually transmitted diseases in the United States. The resulting solutions are shown to be within 2.6% of optimality and lead to a 26% cost saving over current screening practices.
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