Small Stretch Spanners in the Streaming Model: New Algorithms and Experiments

Ausiello, Giorgio; Demetrescu, Camil; Franciosa, Paolo Giulio; Italiano, Giuseppe F.; Ribichini, Andrea

doi:10.1007/978-3-540-75520-3_54

Cited by 3 publications

(8 citation statements)

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“…Our investigation includes the randomized streaming algorithms for computing multiplicative (2k − 1)-spanners by Baswana [9] and by Elkin [19], and the recent (3, 2)-spanner algorithm by Ausiello et al [5]. To assess the performance of the streaming algorithms, we consider as a benchmark an off-line algorithm by Zwick [30].…”

Section: Our Resultsmentioning

confidence: 99%

“…The algorithm proposed by Ausiello et al [5] produces a (3, 2)-spanner or a (2, 1)-spanner of an unweighted graph in one pass over the input stream. The input graph is assumed to be represented as an arbitrary sequence of pairs (x, y), representing edge endpoints.…”

Section: The Algorithm By Ausiello Et Al (A)mentioning

confidence: 99%

“…Recently, a simple deterministic algorithm has been proposed by Ausiello et al [5], that in a single pass over the edge stream computes, for k = 2 and k = 3, an optimal size (k, k − 1)-spanner (i.e., containing O(n 1+1/k ) edges in the worst case) in O(1) amortized processing time per edge. The memory used is O(n 1+1/k ) in the worst case, and the algorithm does not need to know in advance either the total number of vertices or the total number of edges in the graph.…”

Section: Introductionmentioning

confidence: 99%

“…The memory used is O(n 1+1/k ) in the worst case, and the algorithm does not need to know in advance either the total number of vertices or the total number of edges in the graph. At any stage, the algorithm in [5] is able to compute on-line a (k, k − 1)-spanner of the graph scanned so far, within the same time and space bounds. A limit of this algorithm, however, is that it cannot compute spanners with general stretch factor.…”

Section: Introductionmentioning

confidence: 99%

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Graph Spanners in the Streaming Model: An Experimental Study

et al. 2008

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This article reports the results of an extensive experimental analysis of efficient algorithms for computing graph spanners in the data streaming model, where an (α, β)-spanner of a graph G is a subgraph S ⊆ G such that for each pair of vertices the distance in S is at most α times the distance in G plus β. To the best of our knowledge, this is the first computational study of graph spanner algorithms in a streaming setting. We compare experimentally the randomized algorithms proposed by Baswana (http://www.citebase.org/abstract?id=oai:arXiv.org:cs/0611023) and by Elkin (In: Algorithmica (2009) 55: 346-374 347 for general stretch factors with the deterministic algorithm presented by Ausiello et al. (In: ), designed for building small stretch spanners. All the algorithms we implemented work in a data streaming model where the input graph is given as a stream of edges in arbitrary order, and all of them need a single pass over the data. Differently from the algorithm in Ausiello et al., the algorithms in Baswana (http://www.citebase.org/abstract?id=oai:arXiv.org:cs/0611023) and Elkin (In: to know in advance the number of vertices in the graph.The results of our experimental investigation on several input families confirm that all these algorithms are very efficient in practice, finding spanners with stretch and size much smaller than the theoretical bounds and comparable to those obtainable by off-line algorithms. Moreover, our experimental findings confirm that small values of the stretch factor are the case of interest in practice, and that the algorithm by Ausiello et al. tends to produce spanners of better quality than the algorithms by Baswana and Elkin, while still using a comparable amount of time and space resources.

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Section: Our Resultsmentioning

confidence: 99%

Section: The Algorithm By Ausiello Et Al (A)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Graph Spanners in the Streaming Model: An Experimental Study

et al. 2008

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“…Another problem is to devise deterministic streaming algorithm for graph spanners. Recently Ausiello et al [2] designed such an algorithm for spanners of stretch at most 6. Another interesting open problem is to design streaming algorithm for spanners of weighted graphs.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%