Showing papers on "Greedy algorithm published in 1974"

A fundamental problem in vehicle routing

Abstract: An important but difficult combinatorial problem, in general, is to find the optimal route for a single vehicle on a given network. This paper defines a problem type, called the General Routing Problem, and gives an algorithm for its solution. The classical Traveling Salesman Problem and the Chinese Postman Problem are shown to be special limiting cases of the General Routing Problem. The algorithm provides a unified approach to both node and arc oriented routing problems, and exploits special properties of most real transportation networks such as sparsity of the associated adjacency matrix, and the tendency for arc symmetry at many nodes. For node oriented routing problems, this approach tends to produce large reduction in effective problem size.

Improvements of the Held-Karp algorithm for the symmetric traveling-salesman problem.

Abstract: A highly efficient algorithm (HK) devised by Held and Karp for solving the symmetric traveling-salesman problem was presented at the 7th Mathematical Programming Symposium in 1970 and published in Mathematical Programming in 1971. Its outstanding performance is due to a clever exploitation of the relationship between the traveling-salesman problem and minimum spanning trees. However, various improvements of their method have led to a version (IHK) which tends to be some 25 times faster than the original one. Experiments with data selected at random, ranging in size up to 80 cities, show that the computing time for IHK is roughly doubled as the number of cities is increased by 10.

Efficient algorithm for the partitioning of trees

Abstract: This paper describes an algorithm for partitioning a graph that is in the form of a tree. The algorithm has a growth in computation time and storage requirements that is directly proportional to the number of nodes in the tree. Several applications of the algorithm are briefly described. In particular it is shown that the tree partitioning problem frequently arises in the allocation of computer information to blocks of storage. Also, a heuristic method of partitioning a general graph based on this algorithm is suggested.

A heuristic algorithm for mixed-integer programming problems

Abstract: A heuristic algorithm for solving mixed-integer programming problems is proposed. The basic idea is to search good feasible solutions located near the LP optimal solution. It consists of four phases: Phase 0, computation of LP optimal solution; Phase 1, computation of the central trajectory T of the feasible region; Phase 2, search for (integer) feasible solutions along T; Phase 3, improvements of feasible solutions. The computational results are encouraging. For example, randomly generated problems with 50 constraints and 400 variables consumed 2∼3 minutes on a FACOM 230/60. The quality of the obtained solutions seem to be quite high. In fact, for many problems with known optimal solutions, our algorithm was successful in obtaining exact optimal solutions.

Optimal Weighted Ancestry Relationships

Abstract: A solution method is given for a class of practical optimization problems requiring the determination of a consistent partial ordering for sets of objects, events, preferences, and the like. These problems are characterized by the existence of “noisy” or contradictory links of varying strengths. The origin of this class of problems is an anthropological study in which it is desired to specify a global chronological ordering of ancient cemetery data. A mathematical formulation is given which results in a minimum weight feedback model. A heuristic is developed similar to the Greedy algorithm for minimum weight spanning trees which requires only one pass through the network.