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Stochastic Distance in Property Testing

Authors Uri Meir , Gregory Schwartzman, Yuichi Yoshida

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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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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.

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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

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.

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