Class GreedyMultiplicativeSpanner<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:

    public class GreedyMultiplicativeSpanner<V,​E>
    extends Object
    implements SpannerAlgorithm<E>
    Greedy algorithm for $(2k-1)$-multiplicative spanner construction (for any integer k >= 1).

    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.

    Dimitrios Michail