Nearly Tight Spectral Sparsification of Directed Hypergraphs
| Autor: | Oko, Kazusato, Sakaue, Shinsaku, Tanigawa, Shin-ichi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| DOI: | 10.4230/lipics.icalp.2023.94 |
| Popis: | Spectral hypergraph sparsification, an attempt to extend well-known spectral graph sparsification to hypergraphs, has been extensively studied over the past few years. For undirected hypergraphs, Kapralov, Krauthgamer, Tardos, and Yoshida (2022) have proved an ε-spectral sparsifier of the optimal O^*(n) size, where n is the number of vertices and O^* suppresses the ε^{-1} and log n factors. For directed hypergraphs, however, the optimal sparsifier size has not been known. Our main contribution is the first algorithm that constructs an O^*(n²)-size ε-spectral sparsifier for a weighted directed hypergraph. Our result is optimal up to the ε^{-1} and log n factors since there is a lower bound of Ω(n²) even for directed graphs. We also show the first non-trivial lower bound of Ω(n²/ε) for general directed hypergraphs. The basic idea of our algorithm is borrowed from the spanner-based sparsification for ordinary graphs by Koutis and Xu (2016). Their iterative sampling approach is indeed useful for designing sparsification algorithms in various circumstances. To demonstrate this, we also present a similar iterative sampling algorithm for undirected hypergraphs that attains one of the best size bounds, enjoys parallel implementation, and can be transformed to be fault-tolerant. LIPIcs, Vol. 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023), pages 94:1-94:19 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|