Low-Step Multi-commodity Flow Emulators
Authors: 
Bernhard Haeupler, 
D. Ellis Hershkowitz, Jason Li, Antti Roeyskoe, Thatchaphol SaranurakAuthors Info & Claims
Bernhard Haeupler, D. Ellis Hershkowitz, Jason Li, Antti Roeyskoe, Thatchaphol SaranurakAuthors Info & ClaimsPages 71 - 82
Abstract
We introduce the concept of low-step multi-commodity flow emulators for any undirected, capacitated graph. At a high level, these emulators contain approximate multi-commodity flows whose paths contain a small number of edges, shattering the infamous flow decomposition barrier for multi-commodity flow.
We prove the existence of low-step multi-commodity flow emulators and develop efficient algorithms to compute them. We then apply them to solve constant-approximate k-commodity flow in O((m+k)1+є) time. To bypass the O(mk) flow decomposition barrier, we represent our output multi-commodity flow implicitly; prior to our work, even the existence of implicit constant-approximate multi-commodity flows of size o(mk) was unknown.
Our results generalize to the minimum cost setting, where each edge has an associated cost and the multi-commodity flow must satisfy a cost budget. Our algorithms are also parallel.
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Index Terms
- Low-Step Multi-commodity Flow Emulators
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Published In
June 2024
2049 pages
ISBN:9798400703836
DOI:10.1145/3618260
- General Chairs:
- Bojan Mohar,
- Igor Shinkar,
- Program Chair:
- Ryan O'Donnell
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Published: 11 June 2024
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