TY - GEN

T1 - Improved girth approximation in weighted undirected graphs

AU - Kadria, Avi

AU - Roditty, Liam

AU - Sidford, Aaron

AU - Williams, Virginia Vassilevska

AU - Zwick, Uri

N1 - Publisher Copyright:
Copyright © 2023 by SIAM.

PY - 2023

Y1 - 2023

N2 - Let G = (V, E, ℓ) be a n-nodes m-edges weighted undirected graph, where ℓ : E → (0, ∞) is a real length function defined on its edges. Let g be the length of the shortest cycle in G. We present an algorithm that in O(kn1+1/k log n + m(k + log n)) expected running time finds a cycle of length at most 4k/3 g, for every integer k ≥ 1. This improves upon the previous best algorithm that in O((n1+1/k log n+ m) log(nM)) time, where ℓ : E → [1, M] is an integral length function, finds a cycle of length at most 2kg [KRS+22]. For k = 1 our algorithm also improves the result of Roditty and Tov [RT13].

AB - Let G = (V, E, ℓ) be a n-nodes m-edges weighted undirected graph, where ℓ : E → (0, ∞) is a real length function defined on its edges. Let g be the length of the shortest cycle in G. We present an algorithm that in O(kn1+1/k log n + m(k + log n)) expected running time finds a cycle of length at most 4k/3 g, for every integer k ≥ 1. This improves upon the previous best algorithm that in O((n1+1/k log n+ m) log(nM)) time, where ℓ : E → [1, M] is an integral length function, finds a cycle of length at most 2kg [KRS+22]. For k = 1 our algorithm also improves the result of Roditty and Tov [RT13].

UR - http://www.scopus.com/inward/record.url?scp=85170048009&partnerID=8YFLogxK

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85170048009

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 2242

EP - 2255

BT - 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023

PB - Association for Computing Machinery

T2 - 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023

Y2 - 22 January 2023 through 25 January 2023

ER -