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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01 Jan 2005
TL;DR: A history of combinatorial optimization can be found in this article, where the assignment problem was formulated as a linear programming problem that automatically has an integer optimum solution. But it was only recently that it was shown that minimizing a linear functional over the set of doubly stochastic matrices gives a permutation matrix, being the optimum assignment.
Abstract: Publisher Summary This chapter traces the history of combinatorial optimization. As a coherent mathematical discipline, combinatorial optimization is relatively young. Linear programming forms the hinge in the history of combinatorial optimization. Its initial conception by Kantorovich and Koopmans was motivated by combinatorial applications—in particular, in transportation and transshipment. The assignment problem is one of the first investigated combinatorial optimization problems. A breakthrough in solving the assignment problem came when Dantzig showed that the assignment problem can be formulated as a linear programming problem that automatically has an integer optimum solution. The reason is a theorem of Birkhoff [1946] stating that the convex hull of the permutation matrices is equal to the set of doubly stochastic matrices—nonnegative matrices in which each row and column sum is equal to 1. Therefore, minimizing a linear functional over the set of doubly stochastic matrices (which is a linear programming problem) gives a permutation matrix, being the optimum assignment.
247 citations
01 Jan 1990
TL;DR: In this paper, an optimal deterministic online strategy for the k-server problem with real line requests is presented. But it is shown that finding an optimal offline schedule is at least as hard as the assignment problem, and the nonexistence of competitive algorithms for asymmetric two-server and memoryless algorithms for the weighted-cache problem is proved.
Abstract: In the k-server problem, one must choose how k mobile servers will serve each of a sequence of requests, making decisions in an online manner. An optimal deterministic online strategy is exhibited when the requests fall on the real line. For the weighted-cache problem, in which the cost of moving to x from any other point is $w( x )$, the weight of x, an optimal deterministic algorithm is also provided. The nonexistence of competitive algorithms for the asymmetric two-server problem and of memoryless algorithms for the weighted-cache problem is proved. A fast algorithm for oflline computing of an optimal schedule is given, and it is shown that finding an optimal offline schedule is at least as hard as the assignment problem.
244 citations
01 May 1989
TL;DR: Some heuristic channel-assignment algorithms for cellular systems are described, developed, in part, by suitably adapting some of the ideas previously introduced in heuristic graph-coloring algorithms.
Abstract: Some heuristic channel-assignment algorithms for cellular systems are described. These algorithms have yielded optimal, or near-optimal assignments, in many cases. The channel-assignment problem can be viewed as a generalized graph-coloring problem, and these algorithms have been developed, in part, by suitably adapting some of the ideas previously introduced in heuristic graph-coloring algorithms. The channel-assignment problem is formulated as a minimum-span problem, i.e. a problem wherein the requirement is to find the minimum bandwidth necessary to satisfy a given demand. Examples are presented, and algorithm performance results are discussed. >
242 citations
01 Jan 1993
TL;DR: In this paper, a new hybrid procedure that combines genetic operators to existing heuristics is proposed to solve the Quadratic Assignment Problem (QAP), where genetic operators are found to improve the performance of both local search and tabu search.
Abstract: A new hybrid procedure that combines genetic operators to existing heuristics is proposed to solve the Quadratic Assignment Problem (QAP). Genetic operators are found to improve the performance of both local search and tabu search. Some guidelines are also given to design good hybrid schemes. These hybrid algorithms are then used to improve on the best known solutions of many test problems in the literature.
241 citations
TL;DR: The Hungarian linear assignment algorithm is now less sensitive to the range of the cost coefficients, and it is shown that the algorithm is essentially equivalent to assignment algorithms based on shortest augmenting paths.
237 citations