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Approximating the Norms of Graph Spanners

Authors Eden Chlamtáč, Michael Dinitz, Thomas Robinson

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Author Details

Eden Chlamtáč
  • Ben Gurion University of the Negev, Beersheva, Israel
Michael Dinitz
  • Johns Hopkins University, Baltimore, MD, USA
Thomas Robinson
  • Ben Gurion University of the Negev, Beersheva, Israel

Funding

  • Chlamtáč, Eden: Supported in part by ISF grant 1002/14.
  • Dinitz, Michael: Supported in part by NSF awards CCF-1464239 and CCF-1535887.
  • Robinson, Thomas: Supported in part by ISF grant 1002/14.

Cite As Get BibTex

Eden Chlamtáč, Michael Dinitz, and Thomas Robinson. Approximating the Norms of Graph Spanners. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.11

Abstract

The l_p-norm of the degree vector was recently introduced by [Chlamtáč, Dinitz, Robinson ICALP '19] as a new cost metric for graph spanners, as it interpolates between two traditional notions of cost (the sparsity l_1 and the max degree l_infty) and is well-motivated from applications. We study this from an approximation algorithms point of view, analyzing old algorithms and designing new algorithms for this new context, as well as providing hardness results. Our main results are for the l_2-norm and stretch 3, where we give a tight analysis of the greedy algorithm and a new algorithm specifically tailored to this setting which gives an improved approximation ratio.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sparsification and spanners
Keywords
  • Spanners
  • Approximations

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References

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