This paper studies a k-median Steiner forest problem that jointly optimizes the opening of at most k facility locations and their connections to the client locations, so that each client is connected by a path to an o...
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This paper studies a k-median Steiner forest problem that jointly optimizes the opening of at most k facility locations and their connections to the client locations, so that each client is connected by a path to an open facility, with the total connection cost minimized. The problem has wide applications in the telecommunication and transportation industries, but is strongly NP-hard. In the literature, only a 2-approximation algorithm is known, it being based on a Lagrangian relaxation of the problem and using a sophisticated primal-dual schema. In this study, we have developed an improved approximation algorithm using a simple transformation from an optimal solution of a minimum spanning tree problem. Compared with the existing 2-approximation algorithm, our new algorithm not only achieves a better approximation ratio that is easier to be proved, but also guarantees to produce solutions of equal or better quality up to 50 percent improvement in some cases. In addition, for two non-trivial special cases, where either every location contains a client, or all the locations are in a tree-shaped network, we have developed, for the first time in the literature, new algorithms that can solve the problem to optimality in polynomialtime. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
Metabolic networks represent the relationship between chemical reactions and compounds in cells. In useful metabolite production using microorganisms, it is often required to calculate reaction deletion strategies fro...
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Metabolic networks represent the relationship between chemical reactions and compounds in cells. In useful metabolite production using microorganisms, it is often required to calculate reaction deletion strategies from the original network to result in growth coupling, which means the target metabolite production and cell growth are simultaneously achieved. Although simple elementary flux mode (EFM)-based methods are useful for listing such reaction deletions strategies, the number of cases to be considered is often proportional to the exponential function of the size of the network. Therefore, it is desirable to develop methods of narrowing down the number of reaction deletion strategy candidates. In this study, the author introduces the idea of L1 norm minimal modes to consider metabolic flows whose L1 norms are minimal to satisfy certain criteria on growth and production, and developed a fast metabolic design listing algorithm based on it (minL1-FMDL), which works in polynomialtime. Computational experiments were conducted for (1) a relatively small network to compare the performance of minL1-FMDL with that of the simple EFM-based method and (2) a genome-scale network to verify the scalability of minL1-FMDL. In the computational experiments, it was seen that the average value of the target metabolite production rates of minL1-FMDL was higher than that of the simple EFM-based method, and the computation time of minL1-FMDL was fast enough even for genome-scale networks. The developed software, minL1-FMDL, implemented in MATLAB, is available on https://***/(similar to)tamura/software, and can be used for genome-scale metabolic network design for metabolite production.
This paper studies the two-agent vehicle scheduling problems on a line with the constraint that each job is processed after its release time. All jobs belong to agent A or agent B and each job is located at some verte...
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This paper studies the two-agent vehicle scheduling problems on a line with the constraint that each job is processed after its release time. All jobs belong to agent A or agent B and each job is located at some vertex on the line. The vehicle starts from an initial vertex vo to process all jobs. The objective of the problem is to find a route of the vehicle so as to minimize the makespan of agent A under the constraint condition that the makespan of agent B is no more than the threshold value Q. This problem can be expressed by the 3-field scheduling notations as line - l vertical bar r(v(j)), C-max(B) <= Q vertical bar C-max(A), For the problem without release time, we show this problem is solvable in polynomialtime and an O(n) timealgorithm is provided. For the problem with release time, we prove this problem is NP-hard and then, a 3+root 5/2-approximation algorithm is presented. Finally, we conclude the numerical experiments to evaluate the performance of the approximation algorithm.
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We u...
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Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization formulation to simultaneously learn the underlying regression coefficients and the permutation corresponding to the mismatches. The combinatorial structure of the problem leads to computational challenges. We propose and study a simple greedy local search algorithm for this optimization problem that enjoys strong theoretical guarantees and appealing computational performance. We prove that under a suitable scaling of the number of mismatched pairs compared to the number of samples and features, and certain assumptions on problem data;our local search algorithm converges to a nearly-optimal solution at a linear rate. In particular, in the noiseless case, our algorithm converges to the global optimal solution with a linear convergence rate. Based on this result, we prove an upper bound for the estimation error of the parameter. We also propose an approximate local search step that allows us to scale our approach to much larger instances. We conduct numerical experiments to gather further insights into our theoretical results, and show promising performance gains compared to existing approaches.
We study the design of large-scale group testing schemes under a heterogeneous population (i.e., subjects with potentially different risk) and with the availability of multiple tests. The objective is to classify the ...
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We study the design of large-scale group testing schemes under a heterogeneous population (i.e., subjects with potentially different risk) and with the availability of multiple tests. The objective is to classify the population as positive or negative for a given binary characteristic (e.g., the presence of an infectious disease) as efficiently and accurately as possible. Our approach examines components often neglected in the literature, such as the dependence of testing cost on the group size and the possibility of no testing, which are especially relevant within a heterogeneous setting. By developing key structural properties of the resulting optimization problem, we are able to reduce it to a network flow problem under a specific, yet not too restrictive, objective function. We then provide results that facilitate the construction of the resulting graph and finally provide a polynomial time algorithm. Our case study, on the screening of HIV in the United States, demonstrates the substantial benefits of the proposed approach over conventional screening methods. Summary of Contribution: This paper studies the problem of testing heterogeneous populations in groups in order to reduce costs and hence allow for the use of more efficient tests for high-risk groups. The resulting problem is a difficult combinatorial optimization problem that is NP-complete under a general objective. Using structural properties specific to our objective function, we show that the problem can be cast as a network flow problem and provide a polynomial time algorithm.
We prove that on (P-7, banner)-free graphs the maximum weight stable set problem is solvable in polynomialtime. (c) 2007 Elsevier B.V. All rights reserved.
We prove that on (P-7, banner)-free graphs the maximum weight stable set problem is solvable in polynomialtime. (c) 2007 Elsevier B.V. All rights reserved.
The maximum weight stable set problem (MWS) is the weighted version of the maximum stable set problem (MS), which is NP-hard. The class of P-5-free graphs - i.e., graphs with no induced path of five vertices - is the ...
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The maximum weight stable set problem (MWS) is the weighted version of the maximum stable set problem (MS), which is NP-hard. The class of P-5-free graphs - i.e., graphs with no induced path of five vertices - is the unique minimal class, defined by forbidding a single connected subgraph, for which the computational complexity of MS is an open question. At the same time, it is known that NIS can be efficiently solved for (P-5, F) -free graphs, where F is any graph of five vertices different to a C-5. In this paper we introduce some observations on P-5-free graphs, and apply them to introduce certain subclasses of such graphs for which one can efficiently solve MWS. That extends or improves some known results, and implies - together with other known results - that MWS can be efficiently solved for (P-5, F) -free graphs where F is any graph of five vertices different to a C-5. (C) 2006 Elsevier B.V. All rights reserved.
In this paper, we study the single-item lot sizing problem under a capacity reservation contract. A manufacturer is replenished by an external supplier with batch deliveries and a certain capacity is reserved at the s...
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In this paper, we study the single-item lot sizing problem under a capacity reservation contract. A manufacturer is replenished by an external supplier with batch deliveries and a certain capacity is reserved at the supplier level with an advantageous cost. In addition to the classical ordering and inventory holding costs, for each batch ordered under the reserved capacity a fixed cost per batch is incurred;and for batches exceeding this capacity a higher fixed cost per batch is paid, typically through the purchase from the spot market. We identify various NP-hard cases, propose a pseudo-polynomialtime dynamic programming algorithm under arbitrary parameters, show that the problem admits an FPTAS and give polynomial time algorithms for special cases. We finally state a list of open problems for further research. (C) 2016 Elsevier B.V. All rights reserved.
A vertex coloring of a graph G = (V, E) that uses k colors is called an injective k-coloring of G if no two vertices having a common neighbor have the same color. The minimum k for which G has an injective k-coloring ...
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A vertex coloring of a graph G = (V, E) that uses k colors is called an injective k-coloring of G if no two vertices having a common neighbor have the same color. The minimum k for which G has an injective k-coloring is called the injective chromatic number of G. Given a graph G and a positive integer k, the DECIDE INJECTIVE COLORING PROBLEM iS to decide whether G admits an injective k-coloring. It is known that DECIDE INJECTIVE COLORING PROBLEM is NP-complete for bipartite graphs. In this paper, we strengthen this result by showing that this problem remains NP-complete for perfect elimination bipartite graphs, star-convex bipartite graphs and comb-convex bipartite graphs, which are proper subclasses of bipartite graphs. Moreover, we show that for every epsilon > 0, it is not possible to efficiently approximate the injective chromatic number of a perfect elimination bipartite graph within a factor of n(1/3-epsilon) unless ZPP = NP. On the positive side, we propose a linear timealgorithm for biconvex bipartite graphs and O(nm) timealgorithm for convex bipartite graphs for finding the optimal injective coloring. We prove that the injective chromatic number of a chordal bipartite graph can be determined in polynomialtime. It is known that DECIDE INJECTIVE COLORING PROBLEM is NP-complete for chordal graphs. We give a linear timealgorithm for computing the injective chromatic number of proper interval graphs, which is a proper subclass of chordal graphs. DECIDE INJECTIVE COLORING PROBLEM is also known to be NP-complete for split graphs. We show that DECIDE INJECTIVE COLORING PROBLEM remains NP-complete for K-1,K-t-free split graphs for t >= 4 and polynomially solvable for t <= 3. (C) 2020 Elsevier B.V. All rights reserved.
In a graph G = (V, E), a vertex v is an element of V is said to ve-dominate the edges incident on v as well as the edges adjacent to these incident edges on v. A set D subset of V is called a double vertex-edge domina...
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In a graph G = (V, E), a vertex v is an element of V is said to ve-dominate the edges incident on v as well as the edges adjacent to these incident edges on v. A set D subset of V is called a double vertex-edge dominating set if every edge of the graph is ve-dominated by at least two vertices of D. Given a graph G, the double vertex-edge dominating problem, namely Min-DVEDS is to find a minimum double vertex-edge dominating set of G. In this paper, we show that the decision version of Min-DVEDS is NP-complete for chordal graphs. We present a linear timealgorithm to find a minimum double vertexedge dominating set in proper interval graphs. We also show that for a graph having n vertices, Min-DVEDS cannot be approximated within (1 - epsilon) ln n for any epsilon > 0 unless NP subset of Dtime(n(O(log log n))). On positive side, we show that Min-DVEDS can be approximated by a factor of O(ln Delta). Finally, we show that Min-DVEDS is APX-complete for graphs with maximum degree 5.
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