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Perfect Simulation of Las Vegas Algorithms via Local Computation

Authors Xinyu Fu , Yonggang Jiang , Yitong Yin

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LIPIcs.ITCS.2026.63.pdf
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ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Las Vegas algorithms
  • perfect simulation
  • Lovász Local Lemma
  • sampling

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Abstract

The notion of Las Vegas algorithms was introduced by Babai (1979) and can be defined in two ways:  
- In Babai’s original definition, a randomized algorithm is called Las Vegas if it has a finitely bounded running time and certifiable random failure. 
- Another definition widely accepted today is that Las Vegas algorithms refer to zero-error randomized algorithms with random running times.  The equivalence between the two definitions is straightforward. Specifically, for randomized algorithms with certifiable failures, repeatedly running the algorithm until no failure is encountered allows for faithful simulation of the correct output when it executes successfully.
We show that a similar perfect simulation can also be achieved in distributed local computation. Specifically, in the LOCAL model, with a polylogarithmic overhead in time complexity, any Las Vegas algorithm with finitely bounded running time and locally certifiable failures can be converted to a zero error Las Vegas algorithm. This transformed algorithm faithfully reproduces the correct output of the original algorithm in successful executions. This is achieved by a reduction to a distributed sampling problem under the Lovász Local Lemma (LLL), where the objective is to sample from the joint distribution of random variables avoiding all bad events. We then design the first efficient algorithm to solve this sampling problem in the LOCAL model.

Cite As Get BibTex

Xinyu Fu, Yonggang Jiang, and Yitong Yin. Perfect Simulation of Las Vegas Algorithms via Local Computation. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 63:1-63:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.63

Author Details

Xinyu Fu
  • State Key Laboratory for Novel Software Technology, New Cornerstone Science Laboratory, Nanjing University, China
Yonggang Jiang
  • MPI-INF, Saarbrücken, Germany
  • Saarland University, Saarbrücken, Germany
Yitong Yin
  • State Key Laboratory for Novel Software Technology, New Cornerstone Science Laboratory, Nanjing University, China

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