2026-07-26T19:18:18Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11226 2024-03-06T10:47:44Z ddc:004 open_access

Approximating the Norms of Graph Spanners Chlamtáč, Eden Dinitz, Michael Robinson, Thomas Spanners Approximations 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eden Chlamtáč and Michael Dinitz and Thomas Robinson 2019 Is Part Of LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2019.11 urn:nbn:de:0030-drops-112261 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.11 eng https://creativecommons.org/licenses/by/3.0/legalcode