TY - GEN

T1 - Optimal girth approximation for dense directed graphs

AU - Chechik, Shiri

AU - Lifshitz, Gur

N1 - Publisher Copyright:
Copyright © 2021 by SIAM

PY - 2021

Y1 - 2021

N2 - In this paper we provide a Õ(n2) time algorithm that computes a 2-multiplicative approximation of the girth of an n-node m-edge directed graph with non-negative edge weights. We also provide an additional algorithm that computes a 2-multiplicative approximation of the girth in Õ(m√n) time 1. Our results naturally provide algorithms for improved constructions of 4-roundtrip spanners, the analog of spanners in directed graphs. Our algorithm is optimal (up to a log n factor) for dense graphs with m = Θ(n2). For comparison, previously, the best approximation ratio with a similar running time for dense graphs was O(log n log log n) [1]. Moreover, unlike previous algorithms, our algorithm neither assumes integer weights, nor does it depend on the maximum edge weight of the graph.

AB - In this paper we provide a Õ(n2) time algorithm that computes a 2-multiplicative approximation of the girth of an n-node m-edge directed graph with non-negative edge weights. We also provide an additional algorithm that computes a 2-multiplicative approximation of the girth in Õ(m√n) time 1. Our results naturally provide algorithms for improved constructions of 4-roundtrip spanners, the analog of spanners in directed graphs. Our algorithm is optimal (up to a log n factor) for dense graphs with m = Θ(n2). For comparison, previously, the best approximation ratio with a similar running time for dense graphs was O(log n log log n) [1]. Moreover, unlike previous algorithms, our algorithm neither assumes integer weights, nor does it depend on the maximum edge weight of the graph.

UR - http://www.scopus.com/inward/record.url?scp=85105248790&partnerID=8YFLogxK

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AN - SCOPUS:85105248790

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

SP - 290

EP - 300

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

A2 - Marx, Daniel

PB - Association for Computing Machinery

T2 - 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

Y2 - 10 January 2021 through 13 January 2021

ER -