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Partial Order Multiway Search

Published: 13 November 2023 Publication History

Abstract

Partial order multiway search (POMS) is a fundamental problem that finds applications in crowdsourcing, distributed file systems, software testing, and more. This problem involves an interaction between an algorithm 𝒜 and an oracle, conducted on a directed acyclic graph 𝒢 known to both parties. Initially, the oracle selects a vertex t in 𝒢 called the target. Subsequently, 𝒜 must identify the target vertex by probing reachability. In each probe, 𝒜 selects a set Q of vertices in 𝒢, the number of which is limited by a pre-agreed value k. The oracle then reveals, for each vertex qQ, whether q can reach the target in 𝒢. The objective of 𝒜 is to minimize the number of probes. We propose an algorithm to solve POMS in \(O(\log _{1+k} n + \frac{d}{k} \log _{1+d} n)\) probes, where n represents the number of vertices in 𝒢, and d denotes the largest out-degree of the vertices in 𝒢. The probing complexity is asymptotically optimal. Our study also explores two new POMS variants: The first one, named taciturn POMS, is similar to classical POMS but assumes a weaker oracle, and the second one, named EM POMS, is a direct extension of classical POMS to the external memory (EM) model. For both variants, we introduce algorithms whose performance matches or nearly matches the corresponding theoretical lower bounds.

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Published In

cover image ACM Transactions on Database Systems
ACM Transactions on Database Systems  Volume 48, Issue 4
December 2023
71 pages
ISSN:0362-5915
EISSN:1557-4644
DOI:10.1145/3632299
Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 13 November 2023
Online AM: 09 October 2023
Accepted: 14 September 2023
Revised: 29 July 2023
Received: 15 December 2022
Published in TODS Volume 48, Issue 4

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Author Tags

  1. Partial order
  2. graph algorithms
  3. data structures
  4. lower bounds

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  • Deutsche Forschungsgemeinschaft (DFG)

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