Pushing the Online Boolean Matrix-Vector Multiplication Conjecture Off-Line and Identifying Its Easy Cases

Leszek Gąsieniec, Jesper Andreas Jansson, Christos Levcopoulos, Andrzej Lingas, Mia Persson

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

Henzinger et al. posed the so-called Online Boolean Matrix-vector Multiplication (OMv) conjecture and showed that it implies tight hardness results for several basic dynamic or partially dynamic problems [STOC'15]. We first show that the OMv conjecture is implied by a simple off-line conjecture that we call the MvP conjecture. We then show that if the definition of the OMv conjecture is generalized to allow individual (i.e., it might be different for different matrices) polynomial-time preprocessing of the input matrix, then we obtain another conjecture (called the OMvP conjecture) that is in fact equivalent to our MvP conjecture. On the other hand, we demonstrate that the OMv conjecture does not hold in restricted cases where the rows of the matrix or the input vectors are clustered, and develop new efficient randomized algorithms for such cases. Finally, we present applications of our algorithms to answering graph queries.

Original languageEnglish
Pages (from-to)108-118
Number of pages11
JournalJournal of Computer and System Sciences
Volume118
DOIs
Publication statusPublished - 2021

Keywords

  • Boolean matrix
  • Dynamic graph problems
  • Online computation
  • Product of matrix and vector
  • Time complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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