Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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TL;DR: This paper provides an iterative linear programming solution, which finds the maxmin optimal rate assignment and a forwarding schedule that implements the assignment in a low-rate sensor network, and proves that there is one and only one such assignment for a given configuration of the sensor network.
Abstract: The ad hoc deployment of a sensor network causes unpredictable patterns of connectivity and varied node density, resulting in uneven bandwidth provisioning on the forwarding paths. When congestion happens, some sensors may have to reduce their data rates. It is an interesting but difficult problem to determine which sensors must reduce rates and how much they should reduce. This paper attempts to answer a fundamental question about congestion resolution: What are the maximum rates at which the individual sensors can produce data without causing congestion in the network and unfairness among the peers? We define the maxmin optimal rate assignment problem in a sensor network, where all possible forwarding paths are considered. We provide an iterative linear programming solution, which finds the maxmin optimal rate assignment and a forwarding schedule that implements the assignment in a low-rate sensor network. We prove that there is one and only one such assignment for a given configuration of the sensor network. We also study the variants of the maxmin fairness problem in sensor networks.
73 citations
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TL;DR: This paper proposes a new dynamical system model of the route choice behavior at the aggregate, route level for both static and dynamic transportation networks, and presents an Euler-based perturbation method for finding user equilibrium.
Abstract: User equilibrium is a central concept for studying transportation networks, and one can view it as the result of a dynamical process of drivers' route choice behavior. In this paper, based on a definition of O-D First-In-First-Out violation, we propose a new dynamical system model of the route choice behavior at the aggregate, route level for both static and dynamic transportation networks. An equilibrium of such a dynamical system can be a user equilibrium or a partial user equilibrium. We prove that, for static, symmetric traffic assignment problem with fixed or variable demand, only user equilibria are stable for the dynamical system, and the objective function in the mathematical programming formulation (Beckmann, McGuire, and Winsten, 1956) can be considered as the potential energy of the dynamical system. We then present an Euler-based perturbation method for finding user equilibrium and solve two examples for both static and dynamic traffic assignment problems. This new model is simple in form and could be applied to analyze other properties of transportation networks.
73 citations
01 Mar 1983
TL;DR: The state of the art in enumerative solution methods for the traveling salesman problem (TSP) is reviewed, including the results and statistical analysis of some computational experiments designed for the purposes of this review.
Abstract: : This paper reviews the state of the art in enumerative solution methods for the traveling salesman problem (TSP). The introduction (Section 1) discusses the main ingredients of branch and bound methods for the TSP. Sections 2, 3 and 4 discuss classes of methods based on three different relaxations of the TSP: the assignment problem with the TSP cost function, the 1-tree problem with a Lagrangian objective function, and the assignment problem with a Lagrangean objective function. Section 5 briefly reviews some other relaxations of the TSP, while Section 6 discusses the performance of some state of the art computer codes. Besides material from the literature, the paper also includes the results and statistical analysis of some computational experiments designed for the purposes of this review.
73 citations
TL;DR: In this paper, the problem of reassigning some poles of a vibratory system, while keeping the other poles unchanged, is considered, and a family of solutions to the partial pole assignment problem may be obtained by applying multi-input control forces.
73 citations
TL;DR: In this article, it was shown that XA+XBX=HX represents a partially pole assignment problem, and a new method, called the inverse procedure, was proposed to design these controllers.
Abstract: This paper deals with the resolution of equation XA+XBX=HX, which plays a fundamental rule in the design of controllers of linear systems with constrained control by the use of the recently developed concept of positive invariance. It is also shown that this equation represents a partially pole assignment problem. Such resolution allows us to build a new method, called the inverse procedure, to design these controllers. >
73 citations