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Worst-Case and Average-Case Hardness of Hypercycle and Database Problems

Authors Cheng-Hao Fu , Andrea Lincoln , Rene Reyes

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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Database theory
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Hypergraphs
  • hypercycles
  • fine-grained complexity
  • average-case complexity
  • databases

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Abstract

In this paper we present tight lower-bounds and new upper-bounds for hypergraph and database problems. We give tight lower-bounds for finding minimum hypercycles. We give tight lower-bounds for a substantial regime of unweighted hypercycle. We also give a new faster algorithm for longer unweighted hypercycles. We give a worst-case to average-case reduction from detecting a subgraph of a hypergraph in the worst-case to counting subgraphs of hypergraphs in the average-case. We demonstrate two applications of this worst-case to average-case reduction, which result in average-case lower bounds for counting counting hypercycles in random hypergraphs and queries in average-case databases. Our tight upper and lower bounds for hypercycle detection in the worst-case have immediate implications for the average-case via our worst-case to average-case reductions.

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Cheng-Hao Fu, Andrea Lincoln, and Rene Reyes. Worst-Case and Average-Case Hardness of Hypercycle and Database Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 81:1-81:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.81

Author Details

Cheng-Hao Fu
  • Boston University, MA, USA
Andrea Lincoln
  • Boston University, MA, USA
Rene Reyes
  • Boston University, MA, USA

Funding

  • Reyes, Rene: Supported by the National Science Foundation under Grant No.2209194.

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