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Stochastic Distance in Property Testing

Authors Uri Meir , Gregory Schwartzman, Yuichi Yoshida

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Author Details

Uri Meir
  • Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv, Israel
Gregory Schwartzman
  • JAIST, Nomi, Japan
Yuichi Yoshida
  • Principles of Informatics Research Division, National Institute of Informatics, Tokyo, Japan

Funding

  • Schwartzman, Gregory: This work was supported by JSPS KAKENHI Grant Number JP21K17703 and JP21H05850.
  • Yoshida, Yuichi: This work was supported by JSPS KAKENHI Grant Number 20H05965 and 22H05001.

Cite AsGet BibTex

Uri Meir, Gregory Schwartzman, and Yuichi Yoshida. Stochastic Distance in Property Testing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 57:1-57:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.57

Abstract

We introduce a novel concept termed "stochastic distance" for property testing. Diverging from the traditional definition of distance, where a distance t implies that there exist t edges that can be added to ensure a graph possesses a certain property (such as k-edge-connectivity), our new notion implies that there is a high probability that adding t random edges will endow the graph with the desired property. While formulating testers based on this new distance proves challenging in a sequential environment, it is much easier in a distributed setting. Taking k-edge-connectivity as a case study, we design ultra-fast testing algorithms in the CONGEST model. Our introduction of stochastic distance offers a more natural fit for the distributed setting, providing a promising avenue for future research in emerging models of computation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Mathematics of computing → Random graphs
  • Theory of computation → Distributed algorithms
Keywords
  • Connectivity
  • k-edge connectivity

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