Showing papers on "Assignment problem published in 1981"
TL;DR: This mapping problem is formulated in graph theoretic terms and shown to be equivalent, in its most general form, to the graph isomorphism problem.
Abstract: In array processors it is important to map problem modules onto processors such that modules that communicate with each other lie, as far as possible, on adjacent processors. This mapping problem is formulated in graph theoretic terms and shown to be equivalent, in its most general form, to the graph isomorphism problem. The problem is also very similar to the bandwidth reduction problem for sparse matrices and to the quadratic assignment problem.
662 citations
TL;DR: In a large number of randomly generated problems the algorithm has consistently outperformed an efficiently coded version of the Hungarian method by a broad margin.
Abstract: We propose a new algorithm for the classical assignment problem. The algorithm resembles in some ways the Hungarian method but differs substantially in other respects. The average computational complexity of an efficient implementation of the algorithm seems to be considerably better than the one of the Hungarian method. In a large number of randomly generated problems the algorithm has consistently outperformed an efficiently coded version of the Hungarian method by a broad margin. The factor of improvement increases with the problem dimensionN and reaches an order of magnitude forN equal to several hundreds.
276 citations
TL;DR: An algorithm for the asymmetric traveling salesman problem (TSP) using a new, restricted Lagrangean relaxation based on the assignment problem (AP) that can be adapted to the symmetric TSP by using the 2-matching problem instead of AP is described.
Abstract: We describe an algorithm for the asymmetric traveling salesman problem (TSP) using a new, restricted Lagrangean relaxation based on the assignment problem (AP). The Lagrange multipliers are constrained so as to guarantee the continued optimality of the initial AP solution, thus eliminating the need for repeatedly solving AP in the process of computing multipliers. We give several polynomially bounded procedures for generating valid inequalities and taking them into the Lagrangean function with a positive multiplier without violating the constraints, so as to strengthen the current lower bound. Upper bounds are generated by a fast tour-building heuristic. When the bound-strengthening techniques are exhausted without matching the upper with the lower bound, we branch by using two different rules, according to the situation: the usual subtour breaking disjunction, and a new disjunction based on conditional bounds. We discuss computational experience on 120 randomly generated asymmetric TSP's with up to 325 cities, the maximum time used for any single problem being 82 seconds. This is a considerable improvement upon earlier methods. Though the algorithm discussed here is for the asymmetric TSP, the approach can be adapted to the symmetric TSP by using the 2-matching problem instead of AP.
147 citations
TL;DR: A scheduling problem associated with teaching practices at colleges of education is formulated as a 3-dimensional assignment problem and an efficient algorithm for its solution, based on Lagrangean relaxation, is described.
Abstract: A scheduling problem associated with teaching practices at colleges of education is formulated as a 3-dimensional assignment problem. An efficient algorithm for its solution, based on Lagrangean relaxation, is described.
96 citations
TL;DR: In the mathematical model, traffic flows at one junction do not affect costs at others; this is the most important restriction on the work presented here.
Abstract: The paper considers the traffic assignment problem when there are junctions controlled by traffic signals, and the traffic capacity of each junction is limited. We give certain properties of a control policy. If a particular policy possesses these properties then (under natural conditions) any feasible assignment problem has a solution consistent with that policy. In the mathematical model, traffic flows at one junction do not affect costs at others; this is the most important restriction on the work presented here.
68 citations
20 Jan 1981
TL;DR: In this article, the authors describe an algorithm for correlating measurements from several sensors in a dense target environment and show that the correlation problem is similar to the assignment problem in operation research with assisgnment penalties being equal to the sufficient statistic of the generalized likelihood ratio test.
Abstract: In this paper, we describe an algorithm for correlating measurements from several sensors This is a problem area in multiple sensor tracking in a dense target environment It is shown that the correlation problem is similar to the assignment problem in operation research with assisgnment penalties being equal to the sufficient statistic of the generalized likelihood ratio test
48 citations
TL;DR: In this article, the authors consider a network with interactions and capacity constraints at each junction and give conditions on the interactions and constraints which, if satisfied at each separate junction, ensure that any feasible assignment problem has an equilibrium solution.
Abstract: We consider a network with interactions and capacity constraints at each junction. We give conditions on the interactions and constraints which, if satisfied at each separate junction, ensure that any feasible assignment problem has an equilibrium solution. Two illustrative examples are provided; the first arises naturally and does not satisfy our conditions, while the second does satisfy our conditions but is somewhat unnatural.
42 citations
TL;DR: A maximum matching is a matching of maximum cardinality and the set of nodes which take part in such amaximum matching is denoted by Nodes(G) and the cardinality of the matching isDenoted by Card(G).
29 citations
TL;DR: In this paper two generalisations of the time minimising assignment problem are considered, and algorithms are presented to solve these general problems.
Abstract: The time minimising assignment problem is the problem of finding an assignment of n jobs to n facilities, one to each, which minimises the total time for completing all the jobs. The usual assumption made in these problems is that all the jobs are commenced simultaneously. In this paper two generalisations of this assumption are considered, and algorithms are presented to solve these general problems. Numerical examples are worked out illustrating the algorithms.
24 citations
TL;DR: The FORTRAN implementation of an efficient algorithm which solves the Bottleneck Assignment Problem is given and computational results are presented, showing the proposed method to be generally superior to the best known algorithms.
Abstract: The FORTRAN implementation of an efficient algorithm which solves the Bottleneck Assignment Problem is given. Computational results are presented, showing the proposed method to be generally superior to the best known algorithms.
24 citations
TL;DR: In this paper, the problem of determining the non-negative integral matrix all of the row and column sums of which equal n, and which best estimates, in a maximum entropy sense, the table of observed flows is considered.
Abstract: Several combinatorially-based procedures for structuring two-way, as well as three-way, transaction flow matrices have been discussed and illustrated. The inter-relationships between the procedures are of some interest. For example, if the multi-terminal method is applied to a doubly-standardized table, it yields a hierarchical clustering. The assignment algorithm yields cycles—the simplest form of strong components. Strong components are considered as clusters in the IPFPHC procedure. The assignment problem—applied to the logarithms of the observed flows—can be viewed as the solution, for the case n=1, of the problem of determining the non-negative integral matrix all of the row and column sums of which equal n, and which best estimates, in a maximum entropy sense, the table of observed flows. Solutions of the problem for n=1, 2, 3, ... , would yield a series of increasingly complex tables, all of which could be studied with the strong-component analogue of single-linkage clustering. Significance tests for IPFPHC could be developed by studying the distribution of clusters found in random doubly-stochastic tables. These are convex combinations of permutation matrices.
TL;DR: In this article, a design procedure for constructing an appropriate feedback matrix of prescribed structure by successive shifting of selected system poles is presented, based on the Moore-Penrose psoudoin verse.
Abstract: Given a linear time-invariant multivariable system a design procedure is developed, representing a straightforward approach to the problem of constructing an appropriate feedback matrix of prescribed structure by successive shifting of selected system poles. Involving the concept of the Moore-Penrose psoudoin verse, a solution of the linearized definitive equations of the pole assignment problem can be attained, which furthermore tends to favour small feedback gains. The suggested method is simple in theory, direct in application and without ticklish steps. A simple example is included to illustrate the idea and its implications. To demonstrate its applicability and practical usefulness an incomplete state feedback is designed for the example of an 11th-order system.
TL;DR: In this article, a new approach to the pole assignment in linear systems is proposed which is based on unitary or orthogonal transformation of the closed loop system matrix to its Schur canonical form.
TL;DR: A network-based heuristic procedure for solving a class of large non-unimodular assignment-type problems and is developed from certain results concerning multi-commodity network flows and concepts of node-aggregation in networks.
Abstract: We present a network-based heuristic procedure for solving a class of large non-unimodular assignment-type problems. The procedure is developed from certain results concerning multi-commodity network flows and concepts of node-aggregation in networks. Computational experience indicates that problems with over fifteen thousand integer variables can be solved in well under ten seconds using state-of-the-art network optimization software.
TL;DR: An approach to scheduling exams which relates the problem to the classical assignment problem is discussed, and a model developed is a symmetry-constrained assignment model, and the solution method requires use of a branch-and-bound algorithm.
Abstract: Scheduling university examinations is often done with the objective of spreading a student's required examinations over an examination week. That is the equivalent of the problem of minimizing the number of examinations a student must take on any one day. An approach to scheduling exams which relates the problem to the classical assignment problem is discussed. The model developed is a symmetry-constrained assignment model, and the solution method requires use of a branch-and-bound algorithm. Results from application of the algorithm to six semesters of actual data are presented.
TL;DR: In this paper, the authors adopt a generalized Benders' decomposition to solve the combined problem for a system optimized assignment with linear link costs and explicit capacity constraints on link flows, which can be viewed as a modified distribution problem, of gravity form, with a minimax instead of a linear objective function.
Abstract: Much interest has recently been shown in the combination of the distribution and assignment models. In this paper we adopt a generalized Benders' decomposition to solve this combined problem for a system optimized assignment with linear link costs and explicit capacity constraints on link flows. The master problem which is generated is used to show that the combined problem can be viewed as a modified distribution problem, of gravity form, with a minimax instead of a linear objective function. An algorithm for solving the master problem is discussed, and some computational results presented.
TL;DR: This paper presents a proof that for the typical cost function used in the traffic assignment problem, decomposition algorithms converge to an optimal solution.
Abstract: One approach that has been proposed for solving the traffic assignment problem is through decomposition by products or origin-flows. These algorithms try to obtain improved solutions working on one product at a time, while flows corresponding to all other products remain fixed. It is relatively simple to prove that for convex differentiable cost functions, if no improvements can be obtained sequencially in all products, the present solution is optimal. This paper presents a proof that for the typical cost function used in the traffic assignment problem, decomposition algorithms converge to an optimal solution.
31 Aug 1981
TL;DR: It turns out that this “background” optimization is in two precise senses best possible if P≠NP, which is equivalent to finding the maximum of a polynomial in a bounded region.
Abstract: The (bounded) generalized maximum satisfiability problem covers a broad range of NP-complete problems, e.g. it is a generalization of INDEPENDENT SET, LINEAR INEQUALITY, HITTING SET, SET PACKING, MINIMUM COVER, etc. The complexity of finding approximations for problems in this class is analyzed. The results have several interpretations, including the following:
- A general class of existence proofs is made efficiently constructive.
- A class of randomized algorithms is made deterministic and efficient.
- A new class of combinatorial approximation algorithms is introduced, which is based on “background” optimization. Instead of maximizing among all assignments we maximize among expected values for parametrized random solutions. It turns out that this “background” optimization is in two precise senses best possible if P≠NP. The “background optimization” performed is equivalent to finding the maximum of a polynomial in a bounded region.
01 Jan 1981
TL;DR: The time-slot assignment problem for a satellite-switched time-division multiple access system where only a restricted set of all possible switching modes is to be used is studied and an efficient algorithm for finding an optimal assignment is proposed.
Abstract: The time-slot assignment problem for a satellite-switched time-division multiple access system where only a restricted set of all possible switching modes is to be used is studied. An efficient algorithm for finding an optimal assignment is proposed. Also, methods for selecting restricted sets of switching modes are presented.
TL;DR: In this paper, the assignment problem in higher dimensions was generalized to higher dimensions and the hide-and-seek game was extended, and an elegant result due to K. Fan about extrema was generalized.
Abstract: In this paper we generalize the assignment problem in higher dimensions, referring at to another study by the authors. The hide-and-seek game, which is intimately related to the assignment problem, is extended, and an elegant result due to K. Fan about extrema is generalized.
TL;DR: A computer aided method for allocating medical graduates to pre-registration jobs using the Hungarian Algorithm for the assignment problem and it produces a complete solution which is optimal in terms of the numerical criteria specified.
TL;DR: Carpaneto et al. as mentioned in this paper proposed branching and bounding criteria for the asymmetric traveling salesman problem, based on the Toth bounding criterion, and proved its correctness.
Abstract: Erratum to Carpaneto, Giorgio, Paolo Toth. 1980. Branching and bounding criteria for the asymmetric travelling salesman problem. Management Sci.26 7 736-743.
TL;DR: In this article, a geometric programming formulation of the tolerance assignment problem in circuit is presented, where the expressions for optimum component tolerances in circuit are derived and a method is also suggested for the tolerance assignment problem having multiple constraints.
01 Jan 1981
TL;DR: A computer, aided method of allocating newly qualified nurses to their preferred wards using the Hungarian Algorithm for the Assignment Problem, which produces a complete solution which is optimal in terms of the numerical criteria specified.
Abstract: This paper describes a computer, aided method of allocating newly qualified nurses to their preferred wards using the Hungarian Algorithm for the Assignment Problem. The principle advantage of the scheme described here is that it is extremely flexible, allowing various criteria to be taken into consideration for the allocation process. Moreover, it produces a complete solution which is optimal in terms of the numerical criteria specified.