Showing papers on "Greedy algorithm published in 1983"

A Fast Algorithm For The Greedy Interchange For Large-Scale Clustering And Median Location Problems

Abstract: A fast algorithm is described for implementing the greedy interchange heuristic for lise in solving large scale clustering and uncapacitated median location problems. Computational experience is reported for these algorithms on a number of large randomly generated networks and on some difficult problem sets, and comparisons with some other implementations are made. An additional heuristic is proposed for solving these set partitioning problems based on an efficient procedure for achieving the interchange.

Technical Note-An Exact Algorithm for the Time-Constrained Traveling Salesman Problem

Abstract: The time-constrained traveling salesman problem is a variation of the familiar traveling salesman problem that includes time window constraints on the time a particular city, or cities, may be visited. This note presents a concise formulation of the time-constrained traveling salesman problem. The model assumes that the distances of the problem are symmetrical and that the triangle inequality holds. Additionally, the model allows the salesman to wait at a city, if necessary, for a time window to open. The dual of the formulation is shown to be a disjunctive graph model, which is well known from scheduling theory. A longest path algorithm is used to obtain bounding information for subproblems in a branch and bound solution procedure. Computational results are presented for several small to moderate size problems.

Structural properties of greedoids

Abstract: Greedoids were introduced by the authors as generalizations of matroids providing a framework for the greedy algorithm. In this paper they are studied from a structural aspect. Definitions of basic matroid-theoretical concepts such as rank and closure can be generalized to greedoids, even though they loose some of their fundamental properties. The rank function of a greedoid is only “locally” submodular. The closure operator is not monotone but possesses a (relaxed) Steinitz—McLane exchange property. We define two classes of subsets, called rank-feasible and closure-feasible, so that the rank and closure behave nicely for them. In particular, restricted to rank-feasible sets the rank function is submodular. Finally we show that Rado’s theorem on independent transversals of subsets of matroids remains valid for feasible transversals of certain sets of greedoids.

Activity selection games and the minimum-cut problem

Abstract: The connection between the minimum-cut problem in a capacitated network and certain combinatorial problems is well-known. This article presents and analyzes a selection problem in the context of a cooperative game, with emphasis on the key role of associated minimum-cut problems. Each coalition selects economic activities from private activities available to its members and public activities available to all coalitions. For each coalition, a minimum-cut problem finds an optimal selection and the value of the characteristic function. The game is a convex game. Applying the Greedy Algorithm involves solving n minimum-cut problems, where n is the number of players. The solution of n minimum-cut problem determines whether a proposed payoff vector is in the core. An optimal selection of activities varies monotonically with the coalition membership and with the value of each activity. The Shapley value and each extreme point of the core vary monotonically with the value of each activity.

Greedy Colourings of Steiner Triple Systems

Abstract: Three greedy algorithms for colouring the blocks of Steiner triple systems are described; worst-case colourings are studied for each, and their practical use is examined using the eighty Steiner triple systems on fifteen elements.

Database Partitioning in a Cluster of Processors

Abstract: In a distributed database system the partitioning and allocation of the database over the processor nodes of the network can be a critical aspect of the database design effort. In this paper we develop and evaluate algorithms that perform this task in a computationally feasible manner. The network we consider is characterized by a relatively high communication bandwidth, considering the processing and input output capacities in its processors. Such a balance is typical if the processors are connected via busses or local networks. The common constraint that transactions have a specific root node no longer exists, so that there are more distribution choices. However, a poor distribution leads to less efficient computation, higher costs, and higher loads in the nodes or in the communication network so that the system may not be able to handle the required set of transactions.Our approach is to first split the database into fragments which constitute appropriate units for allocation. The fragments to be allocated are selected based on maximal benefit criteria using a greedy heuristic. The assignment to processor nodes uses a first-fit algorithm. The complete algorithm, called GFF, is stated in a procedural form.The complexity of the problem and of its candidate solutions are analyzed and several interesting relationships are proven. Alternate benefit metrics are considered, since the execution cost of the allocation procedure varies by orders of magnitude with the alternatives of benefit evaluation. A mixed benefit evaluation strategy is eventually proposed.A model for evaluation is presented. Two of the strategies are experimentally evaluated, and the reported results support the discussion. The approach should be suitable for other cases where resources have to be allocated subject to resource constraints.

A Heuristic Partitioning Algorithm for a Packaging Problem

Abstract: A heuristic algorithm for solving a problem of a minimum-cost packaging ofN items of the magnitudea j intoM boxes of the capacityb i with a costc ij being assigned to the itemj packing into the boxi is presented. The principal idea of the algorithm consists in the preliminary partitioning of the problem into smaller subproblems and getting an approximate solution by solving these subproblems. A motivation of the heuristic and an application of the algorithm are given.

A Heuristic Routing Algorithm

Abstract: This algorithm, implemented on an inexpensive microcomputer, solved a sophisticated operations research problem.

An Improvement for Weiss's Greedy Heuristic

Abstract: We show that for the greedy heuristic presented by Weiss it is sufficient to compute the matrix X3 rather than Xn to update the transitivity.