In this paper, we present a new polynomial time algorithm for solving the minimum cost network flow problem. This algorithm is based on Edmonds-Karp's capacity scaling and Orlin's excess scaling algorithms. Un...
详细信息
In this paper, we present a new polynomial time algorithm for solving the minimum cost network flow problem. This algorithm is based on Edmonds-Karp's capacity scaling and Orlin's excess scaling algorithms. Unlike these algorithms, our algorithm works directly with the given data and original network, and dynamically adjusts the scaling factor between scaling phases, so that it performs at least one flow augmentation in each phase. Our algorithm has a complexity of O(m(m + n log n) log(B/(m + n))), where n is the number of nodes, m is the number of arcs, and B is the sum of the finite are capacities and supplies in the network. (C) 1999 Elsevier Science B.V. All rights reserved.
We introduce the notion of repeated failure diagnosability for diagnosing the occurrence of a repeated number of failures in discrete event systems. This generalizes the earlier notion of diagnosability that was used ...
详细信息
We introduce the notion of repeated failure diagnosability for diagnosing the occurrence of a repeated number of failures in discrete event systems. This generalizes the earlier notion of diagnosability that was used to diagnose the occurrence of a failure, but from which the information regarding the multiplicity of the occurrence of the failure could not be obtained. It is possible that in some systems the same type of failure repeats a multiple number of times. It is desirable to have a diagnoser which not only diagnoses that such a failure has occurred but also determines the number of times the failure has occurred. To aid such analysis we introduce the notions of K-diagnosability (K failures diagnosability), [1, K]-diagnosabilitv (1 through K failures diagnosability), and [1, infinity]-diagnosability (1 through infinity failures diagnosability). Here the first (resp., last) notion is the weakest (resp., strongest) of all three and the earlier notion of diagnosability is the same as that of K-diagnosability or that of [1, K]-diagnosability with K = 1. We give polynomial algorithms for checking these various notions of repeated failure diagnosability and also present a procedure of polynomial complexity for the on-line diagnosis of repeated failures.
It is well-known that the Travelling Salesman Problem (TSP) is solvable in polynomial time, if the distance matrix fulfills the so-called Demidenko conditions. This paper investigates the closely related Maximum Trave...
详细信息
It is well-known that the Travelling Salesman Problem (TSP) is solvable in polynomial time, if the distance matrix fulfills the so-called Demidenko conditions. This paper investigates the closely related Maximum Travelling Salesman Problem (MaxTSP) on symmetric Demidenko matrices. Somewhat surprisingly, we show that - in strong contrast to the minimization problem - the maximization problem is NP-hard to solve. Moreover, we identify several special cases that are solvable in polynomial time. These special cases contain and generalize several predecessor results by Quintas and Supnick and by Kalmanson. (C) 2000 Elsevier Science B.V. All rights reserved.
We present an extension of Karmarkar's algorithm for solving a system of linear homogeneous equations on the simplex. It is shown that in at most O(nL) steps, the algorithm produces a feasible point or proves that...
详细信息
We present an extension of Karmarkar's algorithm for solving a system of linear homogeneous equations on the simplex. It is shown that in at most O(nL) steps, the algorithm produces a feasible point or proves that the problem has no solution. The complexity is O(n 2 m 2 L) arithmetic operations. The algorithm is endowed with two new powerful stopping criteria.
The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. In its classical setting, solutions are not affected by the warehouse capacity. We study a type of EOQ problem whe...
详细信息
The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. In its classical setting, solutions are not affected by the warehouse capacity. We study a type of EOQ problem where the (maximum) warehouse capacity is a decision variable. Furthermore, we assume that the warehouse cost dominates all the other inventory holding costs. We call this the EOQ-Max problem and the D-EOQ-Max problem, if the product is continuously divisible and discrete, respectively. The EOQ-Max problem admits a closed form optimal solution, while the D-EOQ-Max problem does not because its objective function may have several local minima. We present an optimal polynomial time algorithm for the discrete problem. Construction of this algorithm is supported by the fact that continuous relaxation of the D-EOQ-Max problem provides a solution that can be up to 50% worse than the optimal solution, and this worst-case error bound is tight. Applications of the D-EOQ-Max problem include supply and inventory management, logistics and scheduling. (C) 2009 Elsevier B.V. All rights reserved.
We consider the problem of preemptive scheduling n jobs on two uniform parallel machines. All jobs have equal processing requirements. For each job we are given its due date. The objective is to find a schedule minimi...
详细信息
We consider the problem of preemptive scheduling n jobs on two uniform parallel machines. All jobs have equal processing requirements. For each job we are given its due date. The objective is to find a schedule minimizing total tardiness Sigma T-i. We suggest an O(n log n) algorithm to solve this problem. (C) 2011 Elsevier B.V. All rights reserved.
Integer-valued elements of an integral submodular flow polyhedron Q are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as small as possible, within this, the second ...
详细信息
Integer-valued elements of an integral submodular flow polyhedron Q are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as small as possible, within this, the second largest component is as small as possible, and so on. As a main result, we prove that the set of dec-min integral elements of Q is the set of integral elements of another integral submodular flow polyhedron arising from Q by intersecting a face of Q with a box. Based on this description, we develop a strongly polynomial algorithm for computing not only a dec-min integer-valued submodular flow but even a cheapest one with respect to a linear cost-function. A special case is the problem of finding a strongly connected (or k-edge-connected) orientation of a mixed graph whose in-degree vector is decreasingly minimal. (c) 2022 Elsevier B.V. All rights reserved.
The maximum independent set problem is known to be NP-hard in the class of subcubic graphs, i.e. graphs of vertex degree at most 3. We study complexity of the problem on hereditary subclasses of subcubic graphs. Each ...
详细信息
The maximum independent set problem is known to be NP-hard in the class of subcubic graphs, i.e. graphs of vertex degree at most 3. We study complexity of the problem on hereditary subclasses of subcubic graphs. Each such subclass can be described by means of forbidden induced subgraphs. In case of finitely many forbidden induced subgraphs a necessary condition for polynomial-time solvability of the problem in subcubic graphs (unless P = NP) is the exclusion of the graph S-i,S-j,S-k, which is a tree with three leaves of distance i, j, k from the only vertex of degree 3. Whether this condition is also sufficient is an open question, which was previously answered only for S-1,S-k,S-k-free subcubic graphs and S-2,S-2,S-2 -free subcubic graphs. Combining various algorithmic techniques, in the present paper we generalize both results and show that the problem can be solved in polynomial time for S-2,S-k,S-k-free subcubic graphs, for any fixed value of k. (C) 2020 Elsevier B.V. All rights reserved.
We describe two classes of graphs for which the stability number can be computed in polynomial time. The first approach is based on an iterative procedure which, at each step, builds from a graph G a new graph G' ...
详细信息
We describe two classes of graphs for which the stability number can be computed in polynomial time. The first approach is based on an iterative procedure which, at each step, builds from a graph G a new graph G' which has fewer vertices and has the property that alpha(G') = alpha(G) - 1. For the second class, it can be decided in polynomial time whether there exists a stable set of given size k.
The basic scheduling problem we are dealing with in this paper is the following one. A set of jobs has to be scheduled on a set of parallel uniform machines. Each machine can handle at most one job at a time. Each job...
详细信息
The basic scheduling problem we are dealing with in this paper is the following one. A set of jobs has to be scheduled on a set of parallel uniform machines. Each machine can handle at most one job at a time. Each job becomes available for processing at its release date. All jobs have the same execution requirement and arbitrary due dates. Each machine has a known speed. The processing of any job may be interrupted arbitrarily often and resumed later on any machine. The goal is to find a schedule that minimizes the sum of tardiness, i.e., we consider problem Q vertical bar r(j), p(j) = p, pmtn vertical bar Sigma T-j whose complexity status was open. Recently, Tian et al. (J. Sched. 9: 343-364, 2006) proposed a polynomial algorithm for problem 1 vertical bar r(j), p(j) = p, pmtn vertical bar Sigma T-j. We show that both the problem P vertical bar pmtn vertical bar Sigma T-j of minimizing total tardiness on a set of parallel machines with allowed preemptions and the problem P vertical bar r(j), p(j) = p, pmtn vertical bar Sigma T-j of minimizing total tardiness on a set of parallel machines with release dates, equal processing times and allowed preemptions are NP-hard. Moreover, we give a polynomial algorithm for the case of uniform machines without release dates, i.e., for problem Q vertical bar pj = p, pmtn vertical bar Sigma T-j.
暂无评论