492 research outputs found
Parallel Greedy Spanners
A -spanner of a graph is a subgraph that -approximates pairwise
distances. The greedy algorithm is one of the simplest and most well-studied
algorithms for constructing a sparse spanner: it computes a -spanner with
edges by repeatedly choosing any edge which does not close a
cycle of chosen edges with or fewer edges.
We demonstrate that the greedy algorithm computes a -spanner with edges even when a matching of such edges are added in parallel. In
particular, it suffices to repeatedly add any matching where each individual
edge does not close a cycle with or fewer edges but where adding the
entire matching might. Our analysis makes use of and illustrates the power of
new advances in length-constrained expander decompositions
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