D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone. Experimental analysis of dynamic algorithms for the single source shortest path problem. ACM J. of Exp. Alg., 3, 1998. article 5.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....compares MA and GA on AT T Worldnet backbone network. Right figure shows all solution values produced by the MA. LP lower bound is shown on both figures. changes. For this reason it is sensible to avoid recomputation of all shortest paths. Ramalingam and Reps [6] propose an e#cient algorithm [4] for these dynamic computations. We specialize their procedure tailoring it to our problem. 4. Computational Results Figure 1 illustrates the typical behavior of the MA on a real world network, a realistic version of the AT T Worldnet backbone network. The plot on the left shows that the ....

Frigioni, D., M. Io#reda, U. Nanni, and G. Pasqualone, "Experimental analysis of dynamic algorithms for the single source shortest path problem," ACM J. of Exp. Alg., vol. 3, article 5, 1998.

....to the number of arcs incident to nodes u whose distance d t u to t changes. In our experiments there were typically only very few changes, so the gain was substantial in the order of factor 15 for a 100 node graph. Similar positive experiences with this laziness have been reported in Frigioni et al. 1998). The set of changed distances immediately gives us a set of update arcs to be added to or deleted from A t . We now present a lazy method for finding the changes of loads. We operate with a set M of critical nodes. Initially, M consists of all nodes with an incoming or outgoing update arc. ....

Frigioni, D., M. Ioffreda, U. Nanni, and G. Pasqualone (1998). Experimental analysis of dynamic algorithms for the single-source shortest path problem. ACM Jounal of Experimental Algorithmics 3, article 5.

....number of arcs incident to nodes x whose distance d t x to t changes. In our experiments there were typically only very few changes, so the gain was substantial in the order of factor 20 for a 100 node graph. Similar positive experiences with this laziness have been reported in Frigioni et al. [13]. The set of changed distances immediately gives us a set of update arcs to be added to or deleted from A t . We will now present a lazy method for finding the changes of loads. We will operate with a set M of critical nodes. Initially, M consists of all nodes with an incoming or outgoing ....

D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone, "Experimental analysis of dynamic algorithms for the single-source shortest path problem, " ACM Jounal of Experimental Algorithmics, vol. 3, article 5, 1998.

....model of complexity in which running time is given in terms of a parameter different from input size [12, 14] Their algorithm for maintaining a single source shortest path is similar to ours for the short distances, deletions only case. It has been experimentally analyzed by D. Frigioni et al. [4]. Lower bounds for dynamic transitive closure and shortest paths problems have been considered by several researchers, but in general, the models assumed are too restrictive to imply a lower bound for our algorithms. See [14] for a discussion of these works. The only relevant lower bound is the ....

D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone. Experimental analysis of dynamic algorithms for the singlesource shortest path problem. ACM Jounal of Experimental Algorithmics, 3, article 5, 1998.

....and amortized otherwise. In order to compare the performances of RR and FMN with a static counterpart, we also have implemented a class based on the static algorithm currently implemented in LEDA, that is the Dijkstra s algorithm with Fibonacci heaps. The experiments, whose details are provided in [6], show that both on random graphs and on real world graphs, the dynamic algorithms allow to spend in updates less than 5 of the time required by the static one, and are even better in the case of dense graphs; the number of edge scanned is usually below 0:5 . The two dynamic algorithms provided ....

.... do something with the graph G.deledge(edges[4] G.deledge(edges[5] perform a connectivity query if(dyncon.query(nodes[0] nodes[9] cout dyncon.nodesyes( n ; else cout dyncon.nodesno( n ; do some more graph updates G.newedge(nodes[1] nodes[5] G. newedge(nodes[6],nodes[2] perform a global connectivity query if(dyncon.query( cout dyncon.globalyes( n ; else cout dyncon.globalno( n ; A Software Library of Dynamic Graph Algorithms 135 5 Conclusion and Future Plans Concerning dynamic transitive closure, a preliminary experimental ....

D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone. Experimental analysis of dynamic algorithms for the single source shortest path problem. In Proc. 1st Workshop on Algorithm Engineering (WAE) , September 11-13, 1997, Venice, Italy, 1997.

....and their implementation and practical evaluation. Many papers have been proposed in this field concerning the practical performances of static algorithms for shortest paths (see e.g. 4, 5, 13] but very little is known for the experimental evaluation of dynamic shortest paths algorithms: [8] considers the fully dynamic single source shortest paths problem in digraphs with positive real arc weights. We are not aware of any experimental study in the case of arbitrary arc weights. On the other hand, several papers report on experimental works concerning different dynamic graph problems ....

D. Frigioni, M. Ioffreda, U. Nanni, G. Pasqualone. Experimental Analysis of Dynamic Algorithms for the Single Source Shortest Path Problem. ACM Journal on Experimental Algorithmics, 3:Article 5 (1998).

.... [9, 23, 24, 25] However, despite the number of interesting theoretical results achieved, very little has been done so far with respect to implementations even for the most fundamental problems (the only implementation e ort known to us is concerned with the maintenance of shortest path trees [10, 17]) In this paper, we are making a step forward in bridging the gap between theoretical results for transitive closure and their implementation by studying the practical properties of several dynamic algorithms for this problem. The main goal of the paper is to investigate in practice the ....

D. Frigioni, M. Ioreda, U. Nanni, and G. Pasqualone. Experimental analysis of dynamic algorithms for the single source shortest paths problem. ACM Journal of Experimental Algorithmics, 3:#5, 1998.

.... ) This notion of output complexity can be extended to compute amortized costs [10] We also remark that experiments show that the output complexity is a useful 2 parameter to evaluate the practical efficiency of dynamic algorithms for the single source shortest path problem with positive weights [9]. If the digraph has a k bounded accounting function, then our algorithms require O(k log n) time per output update in the case of weight decrease operations. When the weight of an arc (x; y) is increased we observe that if (x; y) is an arc belonging to the shortest path tree, then the set of ....

....arc weights that are better by a factor of O( p m= log n) than recomputing the new solution from scratch. We are currently implementing the algorithms and we believe that they might be of practical interest; this is partly based on the experiments performed in the case of positive arc weights [9]. An interesting problem is to extend the bounds proposed in the paper to the batch problem, in which an input update is a set of arc modifications, instead of a single arc modification. Another problem is to extend the technique to maintain the all pairs shortest paths in a graph with arbitrary ....

D. Frigioni, M. Ioffreda, U. Nanni, G. Pasqualone. Experimental analysis of dynamic algorithms for the single source shortest path problem. Proc. 1st Work. on Algorithm Engineering, pp. 54--63, 1997.

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D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone. Experimental analysis of dynamic algorithms for the single source shortest path problem. ACM J. of Exp. Alg., 3, 1998. article 5.

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