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Tight cell probe bounds for succinct boolean matrix-Vector multiplication

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The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous important data structure problems, see Henzinger et al. [STOC’15]. In recent work, Larsen and Williams [SODA’17] attacked the problem from the upper bound side and gave a surprising cell probe data structure (that is, we only charge for memory accesses, while computation is free). Their cell probe data structure answers queries in Õ(n7/4) time and is succinct in the sense that it stores the input matrix in read-only memory, plus an additional Õ(n7/4) bits on the side. In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication. We present a new cell probe data structure with query time Õ(n3/2) storing just Õ(n3/2) bits on the side. We then complement our data structure with a lower bound showing that any data structure storing r bits on the side, with n < r < n2 must have query time t satisfying tr = Ω (n3). For r ≤ n, any data structure must have t = Ω (n2). Since lower bounds in the cell probe model also apply to classic word-RAM data structures, the lower bounds naturally carry over. We also prove similar lower bounds for matrix-vector multiplication over F2.

Original languageEnglish
Title of host publicationSTOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
Number of pages10
PublisherAssociation for Computing Machinery
Publication year20 Jun 2018
ISBN (Electronic)9781450355599
Publication statusPublished - 20 Jun 2018
Event50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States
Duration: 25 Jun 201829 Jun 2018


Conference50th Annual ACM Symposium on Theory of Computing, STOC 2018
LandUnited States
ByLos Angeles
SponsorACM Special Interest Group on Algorithms and Computation Theory (SIGACT)
SeriesA C M Symposium on the Theory of Computing. Annual Proceedings

    Research areas

  • Boolean matrix-vector multiplication, Cell probe model, Lower bound, Succinct data structure

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