Near-Optimal Algorithm for Directed Expander Decompositions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929708136923136 |
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| author | Sulser, Aurelio L. Gutenberg, Maximilian Probst |
| author_facet | Sulser, Aurelio L. Gutenberg, Maximilian Probst |
| contents | In this work, we present the first algorithm to compute expander decompositions in an m-edge directed graph with near-optimal time Õ(m). Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains near-optimal update times. Our result improves over previous algorithms of Bernstein-Probst Gutenberg-Saranurak (FOCS 2020), Hua-Kyng-Probst Gutenberg-Wu (SODA 2023) that only obtained algorithms optimal up to subpolynomial factors.
In order to obtain our new algorithm, we present a new push-pull-relabel flow framework that generalizes the classic push-relabel flow algorithm Goldberg-Tarjan (JACM 1988) which was later dynamized for computing expander decompositions in undirected graphs Henzinger-Rao-Wang (SIAM J. Comput. 2020), Saranurak-Wang (SODA 2019). We then show that the flow problems formulated in recent work Hua-Kyng-Probst Gutenberg-Wu (SODA 2023) to decompose directed graphs can be solved much more efficiently in the push-pull-relabel flow framework.
Recently, our algorithm has already been employed to obtain the currently fastest algorithm to compute min-cost flows Van den Brand-Chen-Kyng-Liu-Probst Gutenberg-Sachdeva (FOCS 2024). We further believe that our algorithm can be used to speed-up and simplify recent breakthroughs in combinatorial graph algorithms towards fast maximum flow algorithms Chuzhoy-Khanna (SODA 2024), Chuzhoy-Khanna (STOC 2024), Bernstein-Blikstad-Saranurak-Tu (FOCS 2024). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04542 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Near-Optimal Algorithm for Directed Expander Decompositions Sulser, Aurelio L. Gutenberg, Maximilian Probst Data Structures and Algorithms In this work, we present the first algorithm to compute expander decompositions in an m-edge directed graph with near-optimal time Õ(m). Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains near-optimal update times. Our result improves over previous algorithms of Bernstein-Probst Gutenberg-Saranurak (FOCS 2020), Hua-Kyng-Probst Gutenberg-Wu (SODA 2023) that only obtained algorithms optimal up to subpolynomial factors. In order to obtain our new algorithm, we present a new push-pull-relabel flow framework that generalizes the classic push-relabel flow algorithm Goldberg-Tarjan (JACM 1988) which was later dynamized for computing expander decompositions in undirected graphs Henzinger-Rao-Wang (SIAM J. Comput. 2020), Saranurak-Wang (SODA 2019). We then show that the flow problems formulated in recent work Hua-Kyng-Probst Gutenberg-Wu (SODA 2023) to decompose directed graphs can be solved much more efficiently in the push-pull-relabel flow framework. Recently, our algorithm has already been employed to obtain the currently fastest algorithm to compute min-cost flows Van den Brand-Chen-Kyng-Liu-Probst Gutenberg-Sachdeva (FOCS 2024). We further believe that our algorithm can be used to speed-up and simplify recent breakthroughs in combinatorial graph algorithms towards fast maximum flow algorithms Chuzhoy-Khanna (SODA 2024), Chuzhoy-Khanna (STOC 2024), Bernstein-Blikstad-Saranurak-Tu (FOCS 2024). |
| title | Near-Optimal Algorithm for Directed Expander Decompositions |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2403.04542 |