TY - GEN
T1 - Lightweight Near-Additive Spanners
AU - Gitlitz, Yuval
AU - Neiman, Ofer
AU - Spence, Richard
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - An (α,β)-spanner of a weighted graph G=(V,E), is a subgraph H such that for every u,v∈V, dG(u,v)≤dH(u,v)≤α·dG(u,v)+β. The main parameters of interest for spanners are their size (number of edges) and their lightness (the ratio between the total weight of H to the weight of a minimum spanning tree). In this paper we focus on near-additive spanners, where α=1+ε for arbitrarily small ε>0. We show the first construction of light spanners in this setting. Specifically, for any integer parameter k≥1, we obtain an (1+ε,O(k/ε)k·W(·,·))-spanner with lightness O~(n1/k) (where W(·,·) indicates for every pair u,v∈V the heaviest edge in some shortest path between u, v). In addition, we can also bound the number of edges in our spanner by O(kn1+3/k).
AB - An (α,β)-spanner of a weighted graph G=(V,E), is a subgraph H such that for every u,v∈V, dG(u,v)≤dH(u,v)≤α·dG(u,v)+β. The main parameters of interest for spanners are their size (number of edges) and their lightness (the ratio between the total weight of H to the weight of a minimum spanning tree). In this paper we focus on near-additive spanners, where α=1+ε for arbitrarily small ε>0. We show the first construction of light spanners in this setting. Specifically, for any integer parameter k≥1, we obtain an (1+ε,O(k/ε)k·W(·,·))-spanner with lightness O~(n1/k) (where W(·,·) indicates for every pair u,v∈V the heaviest edge in some shortest path between u, v). In addition, we can also bound the number of edges in our spanner by O(kn1+3/k).
KW - lightness
KW - shortest path
KW - spanners
KW - weighted graph
UR - http://www.scopus.com/inward/record.url?scp=85218447467&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-75409-8_17
DO - 10.1007/978-3-031-75409-8_17
M3 - Conference contribution
AN - SCOPUS:85218447467
SN - 9783031754081
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 236
EP - 250
BT - Graph-Theoretic Concepts in Computer Science - 50th International Workshop, WG 2024, Revised Selected Papers
A2 - Kráľ, Daniel
A2 - Milanič, Martin
PB - Springer Science and Business Media Deutschland GmbH
T2 - 50th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2024
Y2 - 19 June 2024 through 21 June 2024
ER -