An Efficient Semi-Streaming PTAS for Tournament Feedback ArcSet with Few Passes
Anubhav Baweja, Justin Jia, David P. Woodruff

TL;DR
This paper introduces the first semi-streaming polynomial-time approximation scheme for the minimum feedback arc set problem in directed tournaments, achieving near-optimal solutions with few passes and limited memory.
Contribution
It presents a novel semi-streaming PTAS for tournament feedback arc set, improving pass and space efficiency over prior algorithms, and explores related streaming problems.
Findings
Achieves a (1+ε)-approximation in polynomial time with few passes
Provides a new time/space trade-off for 1-pass algorithms
Includes lower bounds and algorithms for related streaming problems
Abstract
We present the first semi-streaming PTAS for the minimum feedback arc set problem on directed tournaments in a small number of passes. Namely, we obtain a -approximation in polynomial time , with passes in space. The only previous algorithm with this pass/space trade-off gave a -approximation (SODA, 2020), and other polynomial-time algorithms which achieved a -approximation did so with quadratic memory or with a linear number of passes. We also present a new time/space trade-off for -pass algorithms that solve the tournament feedback arc set problem. This problem has several applications in machine learning such as creating linear classifiers and doing Bayesian inference. We also provide several additional…
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