G. Amato, G. Cattaneo, and G.F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. In Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'97), pages 314--323, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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 (see e.g. [2, 3, 11]) In this paper we make a step toward this direction and we present the first experimental study of the fully dynamic single source shortest paths problem in digraphs with arbitrary (negative and non negative) arc weights. We implemented and experimented several algorithms for updating shortest ....

G. Amato, G. Cattaneo, and G. F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. In ACM-SIAM Symp. on Discrete Algorithms, pp. 1--10, 1997.

.... of important theoretical results have been obtained for both fully and partially dynamic maintenance of several properties on undirected graphs (see e.g. 12, 13, 14, 15, 22, 31] Recently, an equally important e ort has started on implementing these techniques and showing their practical merits [1, 2]. These were the rst implementations concerning fully dynamic maintenance of certain properties (connectivity, minimum spanning tree) in undirected graphs, as well as the rst implementation of sparsi cation, a technique for speeding up dynamic graph algorithms [13] On the other hand, the ....

G. Amato, G. Cattaneo, and G. F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. In Proc. 8th ACM-SIAM Symposium on Discrete Algorithms, pp. 314-323, 1997.

....for the shortest paths problem (see e.g. 10, 11, 21] but nothing is known for the experimental evaluation of dynamic shortest path algorithms. On the contrary this is not the case for other important dynamic graph problems, as, for example, for connectivity and for minimum spanning tree [3, 5]. In this paper we make a first step toward this direction. We implemented the algorithms proposed by Ramalingam and Reps in [31] denoted as RR) and the one proposed by Frigioni et al. in [18, 19] denoted as FMN) and evaluated the practical performances of those algorithms in a fully dynamic ....

G. Amato, G. Cattaneo, and G. F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. In ACM-SIAM Symposium on Discrete Algorithms, pages 1--10, 1997.

....fast codes based on those asymptotically fast methods are yet to be developed. The existing codes sometimes perform substantially worse than even the ad hoc method of recomputing the minimum spanning tree from scratch whenever a tree edge is deleted (see the experimental results reported by Amato, Cattaneo, and Italiano [1997]) In Section 5 we describe in detail how one can apply operations min in subtree1 and min in subtree2 to the dynamic minimum spanning tree problem, and we also present results from experiments with our dynamic minimum spanning tree codes. All our codes are written in C . Code mst recompute is ....

....and the number of edges in the underlying dynamic graph G = V; E) We assume that the set of nodes V is static, that is, it does not change during the computation. Recently Henzinger and King have improved this bound to O(n 1=3 log n) amortized time per one update [Henzinger and King 1997] Amato, Cattaneo, and Italiano [1997] conducted an extensive empirical study of performance of several methods for maintaining the minimum spanning forest, including various variants of Frederickson s data structure and the sparsi cation method, as well as the ad hoc method Implementation of Dynamic Trees 15 code edge insertions ....

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Amato, G., Cattaneo, G., and Italiano, G. F. 1997. Experimental analysis of dynamic minimum spanning tree algorithms. In Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms (1997).

....opposite poor. It is only recently that some of these algorithms have been implemented in C and tested under the LEDA Extension Package Dynamic Algorithms (LEPDGA) 17] To the best of our knowledge, the only results towards this direction are two papers by G. Amato, G. Cattaneo and G. Italiano [2], and D. Alberts, G. Cattaneo and G. Italiano [1] respectively. In the first of these works, they implemented and tested Frederickson s algorithms [12] and compared them to other dynamic algorithms. In the second work, the dynamic minimum spanning tree based on sparsification by Eppstein, Galil, ....

G. Amato, G. Cattaneo and G. Italiano, "Experimental Analysis of Dynamic Minimum Spanning Tree Algorithms," Proceedings of the 8th Annual ACM--SIAM Symposium on Discrete Algorithms, pp. 314--323, January 1997.

....for code mst recompute. Our results seems to confirm this prediction. Code mst2 is about 2.5 times faster than mst1, correctly reflecting the split of the running time of the splaying operation between updates of the pointers and updates of the min key attributes. Amato, Cattaneo, and Italiano [2] conducted extensive empirical study of the performance of several methods for maintaining the minimum spanning tree, including various variants of Frederickson s data structure [6] and the sparsification method [5] Their code adhoc, which seems to be equivalent to our mst recompute, ....

G. Amato, G. Cattaneo, and G. F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. In Proc. 8th Annual ACM-SIAM Symposium on

....method [5] give a data structure for maintaining the minimumspanning forest in a dynamic graph in O( p n) worst case time per one update (edge insertion or deletion) Recently Henzinger and King [11] have improved this result to O(n 1=3 log n) amortized time per one update. Amato et al. [2] conducted extensive empirical study of the performance of several methods for maintaining the minimumspanning forest, including various variants of Frederickson s data structure and the sparsification method. They results show that their code adhoc, which recomputes the whole minimum spanning ....

....to confirm this prediction. Code mst2 is about 2.5 times faster than mst1, accurately reflecting the split of the running time of the splaying operation between updates of the pointers and updates of the min key attributes. Since our code mst recompute seems to be equivalent to code adhoc from [2] and in our experiment code mst recompute performs clearly worse than code mst2, then code mst2 may actually be quite competitive in practice. 6. Conclusions and further work We have developed implementations for two closely related variants of dynamic trees. Our implementations are based on ....

G. Amato, G. Cattaneo, and G. F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. In Proc. 8th ACM-SIAM Symp. on Discrete Algorithms, 1997.

....practical per55 formances of static algorithms for shortest path problems (see e.g. 6] but nothing is known for the experimental evaluation of dynamic shortest path algorithms. This is not the case for other important dynamic graph problems, as, for example, the minimum spanning tree problem [2, 3]. In this paper we make a first small step in this direction. We implemented the algorithms proposed by Ramalingam and Reps in [15] denoted as RR) and the one proposed by Frigioni, Marchetti and Nanni in [12] FMN) and evaluated the practical performances of those algorithms in a fully dynamic ....

G. Amato, G. Cattaneo, G. F. Italiano, Experimental Analysis of Dynamic Minimum Spanning Tree Algorithms, in Proc. ACM--SIAM Symp. on Discrete Algorithms, 1997, 1--10.

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G. Amato, G. Cattaneo, and G.F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. In Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'97), pages 314--323, 1997.

....URL: http: www.info.uniroma2.it italiano . Part of this work was done while visiting the Max Planck Institut fur Informatik, Im Stadtwald, 66123 Saarbrucken, Germany. 1 Introduction In the last years research in dynamic graph algorithms has been a blossoming field (see e.g. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24]) The main dynamic model that has been considered in the literature is the following. We are given a graph G = V; E) and we wish to maintain some property P in G during edge deletions and edge insertions. We refer to this as the dynamic edge model . If the graph represents a communication ....

G. Amato, G. Cattaneo, G. F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. Proceedings 8th ACM-SIAM Symposium on Discrete Algorithms, 1997, 314--323.

....structures for this problem: Sparsification [5] Frederickson s clustering algorithms [8, 9] and a simple dynamic algorithm which we called adhoc. We have already performed an extensive empirical study on the performance of these data structures, and we refer the interested reader to reference [2] for the details. All our algorithms support adding and deleting edges, MST membership queries for edges, and a query returning the current MST. To improve the flexibility and reusability of our code, we choose to maintain the edge costs as an external data structure. This data structure can be ....

....2 dimensional topology trees to achieve a time bound of O(m 1=2 ) per update. All these algorithms are quite complicated, and we were the first to be surprised by the fact that they still show some practical value. We refer the reader to [8, 9] for all the details of these algorithms, and to [2] for their implementation and experimental analysis. In this release of the library, we provide the implementation which was the fastest in the experiments. We mainly use it as an underlying algorithm for sparsification, the technique we introduce next. Sparsification [5] is a general technique ....

[Article contains additional citation context not shown here]

G. Amato, G. Cattaneo and G. F. Italiano. Experimental Analysis of Dynamic Minimum Spanning Tree Algorithms. In Proc. 8th Annual ACM--SIAM Symposium on Discrete Algorithms (SODA 97), pp. 314--323, 1997.

....are not yet offered by existing libraries, and whose implementation may be of independent interest to these libraries. Second, we designed and implemented a version of simple sparsification that operates on dynamic algorithms (the version described in this paper only operates on static algorithms) [5]. We used this version of simple sparsification on top of existing dynamic algorithms, such as Frederickson s dynamic data structures [14, 15] for minimum spanning trees. The algorithms by Frederickson are sophisticated algorithms, for which no implementation was previously available, and that ....

....as Frederickson s dynamic data structures [14, 15] for minimum spanning trees. The algorithms by Frederickson are sophisticated algorithms, for which no implementation was previously available, and that required a great deal of implementation effort. We refer the interested reader to reference [5] for details on how the asymptotically efficient methods obtained by Frederickson s algorithms, run with simple sparsification on top of them, can play an important role in practice as well. Further investigation in this direction, and better tuning of sparsification is still under development. ....

G. Amato, G. Cattaneo, G. F. Italiano, "Experimental analysis of dynamic minimum spanning tree algorithms". Proc. 8th ACM-SIAM Symp. on Discrete Algorithms (SODA 97), New Orleans, USA, 5-7 January 1997, 314--323.

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G. Amato, G. Cattaneo and G.F. Italiano, "Experimental analysis of dynamic minimum spanning tree algorithms," Proc. 8th ACM-SIAM Annual Symp. on Disc. Algorithms (SODA), pp. 314--323, 1997.

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