Local Computation of Nearly Additive Spanners

Abstract. An (α, β)-spanner of a graph G is a subgraph H that approximates distances in G within a multiplicative factor α and an additive error β, ensuring that for any two nodes u, v, dH(u, v) ≤ α·dG(u, v)+ β. This paper concerns algorithms for the distributed deterministic construction of a sparse (α, β)-spanner H for a given graph G and distortion parameters α and β. It first presents a generic distributed algorithm that in constant number of rounds constructs, for every n-node graph and integer k ≥ 1, an (α, β)-spanner of O(βn1+1/k ) edges, where α and β are constants depending on k. For suitable parameters, this algorithm provides a (2k − 1, 0)-spanner of at most kn1+1/k edges in k rounds, matching the performances of the best known distributed algorithm by Derbel et al. (PODC ’08). For k = 2 and constant ε > 0, it can also produce a (1 + ε, 2 − ε)-spanner of O(n3/2 ) edges in constant time. More interestingly, for every integer k > 1, it can c...

• Type: Conference
• Year: 2009
• Where: WDAG
• Authors: Bilel Derbel, Cyril Gavoille, David Peleg, Laurent Viennot
• Keywords: WDAG 2009