In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time. In practical settings, for example, in evacuation or tran...
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In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time. In practical settings, for example, in evacuation or transportation planning, the problem parameters might not be known exactly a priori. It is therefore of interest to consider robust versions of these problems in which travel times and/or capacities of arcs depend on a certain scenario. In this article, minmax versions of robust quickest path problems are investigated and, depending on their complexity status, exact algorithms or fully polynomial-time approximation schemes are proposed. (c) 2012 Wiley Periodicals, Inc. NETWORKS, Vol. 60(4), 253-258 2012
We consider the problem of scheduling a set of dependent jobs on a single machine with the maximum completion time criterion. The processing time of each job is variable and decreases linearly with respect to the star...
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We consider the problem of scheduling a set of dependent jobs on a single machine with the maximum completion time criterion. The processing time of each job is variable and decreases linearly with respect to the starting time of the job. Applying a uniform approach based on the calculation of ratios of expressions that describe total processing times of chains of jobs, we show basic properties of the problem. On the basis of these properties, we prove that if precedence constraints among jobs are in the form of a set of chains, a tree, a forest or a series-parallel digraph, the problem can be solved in O(n log n) time, where n denotes the number of the jobs. (C) 2010 Elsevier Inc. All rights reserved.
We consider the bipartite unconstrained 0-1 quadratic programming problem (BQP01) which is a generalization of the well studied unconstrained 0-1 quadratic programming problem (QP01). BQP01 has numerous applications a...
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We consider the bipartite unconstrained 0-1 quadratic programming problem (BQP01) which is a generalization of the well studied unconstrained 0-1 quadratic programming problem (QP01). BQP01 has numerous applications and the problem is known to be MAX SNP hard. We show that if the rank of an associated m x n cost matrix Q = (q(ij)) is fixed, then BQP01 can be solved in polynomial time. When Q is of rank one, we provide an O(n log n) algorithm and this complexity reduces to O(n) with additional assumptions. Further, if q(ij) = a(i) + b(j) for some a(i) and b(j), then BQP01 is shown to be solvable in O(mn log n) time. By restricting m = O(log n), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m = O(k root n) for a fixed k. Finally, if the minimum number of rows and columns to be deleted from Q to make the remaining matrix non-negative is O(log n), then we show that BQP01 is polynomially solvable but it is NP-hard if this number is O(k root n) for any fixed k. (C) 2015 Elsevier B.V. All rights reserved.
In this paper, we deal with primal-dual interior point methods for solving the linear programming problem. We present a short-step and a long-step path-following primal-dual method and derive polynomial-time bounds fo...
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In this paper, we deal with primal-dual interior point methods for solving the linear programming problem. We present a short-step and a long-step path-following primal-dual method and derive polynomial-time bounds for both methods. The iteration bounds are as usual in the existing literature, namely O(square-root nL) iterations for the short-step variant and O(nL) for the long-step variant. In the analysis of both variants, we use a new proximity measure, which is closely related to the Euclidean norm of the scaled search direction vectors. The analysis of the long-step method depends strongly on the fact that the usual search directions form a descent direction for the so-called primal-dual logarithmic barrier function.
An instance of the quadratic assignment problem (QAP) with cost matrix Q is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix C such that for each assignment, ...
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An instance of the quadratic assignment problem (QAP) with cost matrix Q is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix C such that for each assignment, the QAP and LAP objective function values are identical. The QAP linearization problem can be solved in O(n(4)) time. However, for the special cases of Koopmans-Beckmann QAP and the multiplicative assignment problem the input size is of Omega(n(2)). We show that the QAP linearization problem for these special cases can be solved in O(n(2)) time. For symmetric Koopmans-Beckmann QAP, Bookhold [I. Bookhold, A contribution to quadratic assignment problems, Optimization 21 (1990) 933-943.] gave a sufficient condition for linearizability and raised the question if the condition is necessary. We show that Bookhold's condition is also necessary for linearizability of symmetric Koopmans-Beckmann QAP. (C) 2013 Elsevier B.V. All rights reserved.
Most existing prevention methods tackle the deadlock issue arising in flexible manufacturing systems modeled with Petri nets by adding monitors and arcs. Instead, this paper presents a new one based on a characteristi...
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Most existing prevention methods tackle the deadlock issue arising in flexible manufacturing systems modeled with Petri nets by adding monitors and arcs. Instead, this paper presents a new one based on a characteristic structure of (WSPR)-P-3, an extension of System of Simple Sequential Processes with Resources ((SPR)-P-3) with weighted arcs. The numerical relationships among weights. and between weights and initial markings are investigated based on simple circuits of resource places, which are the simplest structure of circular wait, rather than siphons A (WSPR)-P-3 satisfying a proposed restriction is inherently deadlock-free and live by configuring its initial markings A set of polynomial algorithms are developed to implement the proposed method. Several examples are used to illustrate them (C) 2010 Elsevier Ltd. All rights reserved.
We consider no-wait production processes, where identical products are processed sequentially on n machines and transported by programmable hoists. We present an O(n(5)) algorithm that determines the minimum number of...
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We consider no-wait production processes, where identical products are processed sequentially on n machines and transported by programmable hoists. We present an O(n(5)) algorithm that determines the minimum number of hoists required for all possible cycle-times;given the number of hoists, it also finds the minimum-time cyclic hoist-schedule. (c) 2005 Elsevier B.V. All rights reserved.
A variant of the High Multiplicity Multiprocessor Scheduling Problem with C job lengths is considered, in which jobs can be processed only by machines not greater than a given index. When C = 2, polynomial algorithms ...
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A variant of the High Multiplicity Multiprocessor Scheduling Problem with C job lengths is considered, in which jobs can be processed only by machines not greater than a given index. When C = 2, polynomial algorithms are proposed, for the feasibility version of the problem and for maximizing the number of scheduled jobs.
Many vertex-partitioning problems can be expressed within a general framework introduced by Telle and Proskurowski. They showed that optimization problems in this framework can be solved in polynomial time on classes ...
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Many vertex-partitioning problems can be expressed within a general framework introduced by Telle and Proskurowski. They showed that optimization problems in this framework can be solved in polynomial time on classes of graphs with bounded tree-width. In this paper, we consider a very similar framework, in relationship with more general classes of graphs: we propose a polynomial time algorithm on classes of graphs with bounded clique-width for all the optimization problems in our framework. These classes of graphs are more general than the classes of graphs with bounded tree-width in the sense that classes of graphs with bounded tree-width have also bounded clique-width (but not necessarily the inverse). Our framework includes problems such as independent (dominating) set, p-dominating set, induced bounded degree subgraph, induced p-regular subgraph, perfect matching cut, graph k-coloring and graph list-k-coloring with cardinality constraints (fixed k). This paper thus provides a second (distinct) framework within which the optimization problems can be solved in polynomial time on classes of graphs with bounded clique-width, after a first framework (called MS1) due to the work of Courcelle, Makowsky and Rotics (for which they obtained a linear time algorithm). (C) 2002 Elsevier Science B.V. All rights reserved.
The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown ...
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The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown that the feasibility variant of the project scheduling problem is NP-complete. Moreover, polynomial-time scheduling algorithms are devised for the three cases where the occurrence time sequence of all events or the consuming events or the producing events is given in advance. By enumerating these sequences (called linear orders), one obtains a list-scheduling based algorithm for minimizing the makespan of a project scheduling problem with production and consumption of resources. (C) 2009 Elsevier B.V. All rights reserved.
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