Showing papers on "Assignment problem published in 1969"

Traffic assignment problem for a general network

Abstract: A tra ns portatio n network is co ns ide red . The traffic de mands assoc iat ed wit h pairs of nodes and the (convex) trave ling cos t functions associat ed with the links a re assumed give n. The twu prob le ms of findin g the traffi c patte rn s whi c h e ither minimize the total cos t or equilibrate the use rs' cos ts are formulated , and a lgo rithms are co ns truc ted for the so lutio n of these prob lems.

One-Dimensional Space Allocation: An Ordering Algorithm

Abstract: The space-allocation problem arises when an architect tries to arrange rooms of fixed area but unspecified shape on a floor plan in such a way as to minimize a given linear combination of the distances between all pairs of rooms. In one dimension, this is the problem of ordering line segments along a simple axis or rooms along one side of a corridor. This paper devises an efficient branch-and-bound algorithm for finding the optimal ordering, and shows that the algorithm can solve one special type of facilities-to-locations assignment problem. Space allocation in two dimensions is also discussed briefly.

A Graph-Theoretic Approach to a Class of Integer-Programming Problems

Abstract: This paper presents an efficient algorithm for finding a minimum-weight generalized matching in a weighted bipartite graph. Computational evidence is given that indicates that the time required to find a least-cost assignment of n jobs to n workers goes roughly as n2 for 10 ≦ n ≦ 50. It is shown that this algorithm can be used to solve effectively the well known transportation problem of integer programming where the objective function is convex-separable. Finally, the paper gives an algorithm that applies the same concept to a graph that is not necessarily bipartite.

An experimental evaluation of some methods of solving the assignment problem

Abstract: : Computational experiments were conducted with three methods for solving the assignment problem: Kuhn's Hungarian method, a primal method due to Balinski and Gomory, and a negative cycle method proposed by Klein. Kuhn's method is seen to be the best of the three.

Realization of Sequential Machines with Threshold Elements

Abstract: The state assignment problem for finite-state sequential machines is examined in the context of threshold logic. An algorithm is developed for assigning binary codes to the states, inputs, and outputs so that the state variable and output variable functions satisfy the necessary condition of 2-assumability that they be linearly separable. The algorithm deals with 2-block partitions by which the assignments are made. First those partitions which cannot be used are computed. For each of the remaining partitions, a list is compiled of those partitions of which one must be used if the given partition is used. Finally, a method is given for constructing the sets of partitions satisfying these constraints and having zero product. Code assignments made by these partition sets will induce 2-asummable functions.