Pushing the Online Boolean Matrix-vector Multiplication conjecture off-line and identifying its easy cases

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • University of Liverpool
  • Hong Kong Polytechnic University
  • Malmö University
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)

Nyckelord

  • Boolean matrix, Product of matrix and vector, Dynamic graph problems, Online computation, Time complexity
Originalspråkengelska
Sidor (från-till)108-118
Antal sidor11
TidskriftJournal of Computer and System Sciences
Volym118
StatusPublished - 2021 jun
PublikationskategoriForskning
Peer review utfördJa