TY - GEN

T1 - Algorithmic trade-offs for girth approximation in undirected graphs

AU - Kadria, Avi

AU - Roditty, Liam

AU - Sidford, Aaron

AU - Williams, Virginia Vassilevska

AU - Zwick, Uri

N1 - Publisher Copyright:
Copyright © 2022 by SIAM Unauthorized reproduction of this article is prohibited.

PY - 2022

Y1 - 2022

N2 - We present several new effcient algorithms for approximating the girth, g, of weighted and unweighted n-vertex, m-edge undirected graphs. For undirected graphs with polynomially bounded, integer, non-negative edge weights, we provide an algorithm that for every integer k 1, runs in eO(m + n1+1=k log g) time and returns a cycle of length at most 2kg. For unweighted, undirected graphs we present an algorithm that for every k 1, runs in eO (n1+1=k) time and returns a cycle of length at most 2kdg=2e, an almost k-approximation. Both algorithms provide trade-off-s between the running time and the quality of the approximation. We also obtain faster algorithms for approximation factors better than 2, and improved approximations when the girth is odd or small (e.g., 3 and 4).

AB - We present several new effcient algorithms for approximating the girth, g, of weighted and unweighted n-vertex, m-edge undirected graphs. For undirected graphs with polynomially bounded, integer, non-negative edge weights, we provide an algorithm that for every integer k 1, runs in eO(m + n1+1=k log g) time and returns a cycle of length at most 2kg. For unweighted, undirected graphs we present an algorithm that for every k 1, runs in eO (n1+1=k) time and returns a cycle of length at most 2kdg=2e, an almost k-approximation. Both algorithms provide trade-off-s between the running time and the quality of the approximation. We also obtain faster algorithms for approximation factors better than 2, and improved approximations when the girth is odd or small (e.g., 3 and 4).

UR - http://www.scopus.com/inward/record.url?scp=85128541195&partnerID=8YFLogxK

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AN - SCOPUS:85128541195

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

SP - 1471

EP - 1492

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2022

PB - Association for Computing Machinery

Y2 - 9 January 2022 through 12 January 2022

ER -