TY - GEN
T1 - Approximating the norms of graph spanners
AU - Chlamtáč, Eden
AU - Dinitz, Michael
AU - Robinson, Thomas
N1 - Funding Information:
Funding Eden Chlamtáč: Supported in part by ISF grant 1002/14. Michael Dinitz: Supported in part by NSF awards CCF-1464239 and CCF-1535887. Thomas Robinson: Supported in part by ISF grant 1002/14.
Funding Information:
Eden Chlamt??: Supported in part by ISF grant 1002/14. Michael Dinitz: Supported in part by NSF awards CCF-1464239 and CCF-1535887. Thomas Robinson: Supported in part by ISF grant 1002/14.
Publisher Copyright:
© Eden Chlamtáč, Michael Dinitz, and Thomas Robinson.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - The ℓp-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 ℓ1 and the max degree ℓ∞) 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 ℓ2-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.
AB - The ℓp-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 ℓ1 and the max degree ℓ∞) 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 ℓ2-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.
KW - Approximations
KW - Spanners
UR - http://www.scopus.com/inward/record.url?scp=85072856788&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.APPROX-RANDOM.2019.11
DO - 10.4230/LIPIcs.APPROX-RANDOM.2019.11
M3 - Conference contribution
AN - SCOPUS:85072856788
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
A2 - Achlioptas, Dimitris
A2 - Vegh, Laszlo A.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
Y2 - 20 September 2019 through 22 September 2019
ER -