Fast deterministic distributed algorithms for sparse spanners

  • Authors:

  • Bilel Derbel;Cyril Gavoille

  • Affiliations:

  • Laboratoire Bordelais de Recherche en Informatique, Université de Bordeaux, 351 Cours de la Libération, 33405 Talence, France;Laboratoire Bordelais de Recherche en Informatique, Université de Bordeaux, 351 Cours de la Libération, 33405 Talence, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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Abstract

This paper concerns the efficient construction of sparse and low stretch spanners for unweighted arbitrary graphs with n nodes. All previous deterministic distributed algorithms, for constant stretch spanners of o(n^2) edges, have a running time @W(n^@e) for some constant @e0 depending on the stretch. Our deterministic distributed algorithms construct constant stretch spanners of o(n^2) edges in o(n^@e) time for any constant @e0. More precisely, in Linial's free model a.k.a LOCAL model, we construct in n^O^(^1^/^l^o^g^n^) time, for every graph, a (3,2)-spanner of O(n^3^/^2) edges, i.e., a spanning subgraph in which the distance is at most 3 times the distance of the original graph plus 2. The result is extended to (@a"k,@b"k)-spanners with O(n^1^+^1^/^klogk) edges for every integer parameter k=1, where @a"k+@b"k=O(k^l^o^g^"^2^5). If the minimum degree of the graph is @W(n), then, in the same time complexity, a (5,4)-spanner with O(n) edges can be constructed.