V - the graph vertex typeE - the graph edge typepublic class GreedyMultiplicativeSpanner<V,E> extends Object implements SpannerAlgorithm<E>
The spanner is guaranteed to contain $O(n^{1+1/k})$ edges and the shortest path distance between any two vertices in the spanner is at most $2k-1$ times the corresponding shortest path distance in the original graph. Here n denotes the number of vertices of the graph.
The algorithm is described in: Althoefer, Das, Dobkin, Joseph, Soares. On Sparse Spanners of Weighted Graphs. Discrete Computational Geometry 9(1):81-100, 1993.
If the graph is unweighted the algorithm runs in $O(m n^{1+1/k})$ time. Setting $k$ to infinity will result in a slow version of Kruskal's algorithm where cycle detection is performed by a BFS computation. In such a case use the implementation of Kruskal with union-find. Here n and m are the number of vertices and edges of the graph respectively.
If the graph is weighted the algorithm runs in $O(m (n^{1+1/k} + n \log n))$ time by using Dijkstra's algorithm. Edge weights must be non-negative.
SpannerAlgorithm.Spanner<E>, SpannerAlgorithm.SpannerImpl<E>| Constructor and Description |
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GreedyMultiplicativeSpanner(Graph<V,E> graph,
int k)
Constructs instance to compute a $(2k-1)$-spanner of an undirected graph.
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| Modifier and Type | Method and Description |
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SpannerAlgorithm.Spanner<E> |
getSpanner()
Computes a graph spanner.
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public GreedyMultiplicativeSpanner(Graph<V,E> graph, int k)
graph - an undirected graphk - positive integer.IllegalArgumentException - if the graph is not undirectedIllegalArgumentException - if k is not positivepublic SpannerAlgorithm.Spanner<E> getSpanner()
SpannerAlgorithmgetSpanner in interface SpannerAlgorithm<E>Copyright © 2019. All rights reserved.