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Local routing in a tree metric 1-spanner

Author

Listed:
  • Milutin Brankovic

    (University of Sydney)

  • Joachim Gudmundsson

    (University of Sydney)

  • André van Renssen

    (University of Sydney)

Abstract

Solomon and Elkin (SIAM J Discret Math 28(3):1173–1198, 2014) constructed a shortcutting scheme for weighted trees which results in a 1-spanner for the tree metric induced by the input tree. The spanner has logarithmic lightness, logarithmic diameter, a linear number of edges and bounded degree (provided the input tree has bounded degree). This spanner has been applied in a series of papers devoted to designing bounded degree, low-diameter, low-weight $$(1+\epsilon )$$ ( 1 + ϵ ) -spanners in Euclidean and doubling metrics. In this paper, we present a simple local routing algorithm for this tree metric spanner. The algorithm has a routing ratio of 1, is guaranteed to terminate after $$O(\log n)$$ O ( log n ) hops and requires $$O(\varDelta \log n)$$ O ( Δ log n ) bits of storage per vertex where $$\varDelta $$ Δ is the maximum degree of the tree on which the spanner is constructed. This local routing algorithm can be adapted to a local routing algorithm for a doubling metric spanner which makes use of the shortcutting scheme.

Suggested Citation

  • Milutin Brankovic & Joachim Gudmundsson & André van Renssen, 2022. "Local routing in a tree metric 1-spanner," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2642-2660, November.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:4:d:10.1007_s10878-021-00784-4
    DOI: 10.1007/s10878-021-00784-4
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