Showing papers on "Prim's algorithm published in 1973"

A unified algorithm for designing multidrop teleprocessing networks

Abstract: The problem of designing minimum cost multidrop lines which connect remote terminals to a concentrator or a central data processing computer is studied. In some cases, optimal solutions can be obtained by using either linear integer programming or a branch-bound method. These approaches are not practical since they lack flexibility and require an enormous amount of computer time for most practical problems. As a consequence, heuristic algorithms have been developed by various authors. In this paper, we point out that all of these algorithms fall into the class of minimum spanning tree problems, constrained by traffic or response time requirements. The difference between them is mainly the sequential order with which a branch or a line is selected into the tree. Without the constraints, all algorithms converge to a minimum spanning tree. With the constraints, they form different sub-trees. Most of the algorithms can be unified into a modified Kruskal's minimum spanning tree algorithm.In the modified algorithm, a weight is associated with each terminal. Let Wi be the weight associated with terminal i, and dij be the cost for the line directed from terminal i to terminal j. When the algorithm fetches the cost for the line, it replaces it with dij - wi In some cases, Wi's need to be readjusted in the middle of the algorithm. The difference between all existing heuristic algorithms is in the way wi's are defined. If wi is zero for all i, the algorithm reduces to the unmodified Kruskal's algorithm; if wi is set to zero whenever a line incident to terminal i is selected as a tree branch, the algorithm reduces to Prim's minimum spanning tree algorithm.An extension of the algorithm to the solution of an associated problem of partitioning the terminals with respect to a predetermined set of concentrators, multiplexers, terminal interface processors, or central computers is also derived.The efficiency of an algorithm depends greatly on how it is implemented. The computational complexity of the unified algorithm is in the order of N2 log N for the most general case, where N is the number of terminals. By using good heuristics, it reduces to K1 K log N + K2 N, where K1 and K2 are constants, for many practical applications. The algorithm has been applied to large networks with over 1,000 terminals, yielding excellent results and using only 15 seconds of computer time on a CDC 6600 computer.Designs obtained by using different wi's are compared.