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3D Rectangulations and Geometric Matrix Multiplication

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Author

Summary, in English

The problem of partitioning an input rectilinear polyhedron P into a minimum number of 3D rectangles is known to be NP-hard. We first develop a 4-approximation algorithm for the special case in which P is a 3D histogram. It runs in O(m log m) time, where m is the number of corners in P. We then apply it to compute the arithmetic matrix product of two n x n matrices A and B with nonnegative integer entries, yielding a method for computing A x B in (O) over tilde (n(2) + min{rArB, n min{rA, rB}}) time, where (O) over tilde suppresses polylogarithmic (in n) factors and where rA and rB denote the minimum number of 3D rectangles into which the 3D histograms induced by A and B can be partitioned, respectively.

Publishing year

2014

Language

English

Pages

65-78

Publication/Series

Algorithms and Computation, ISAAC 2014

Volume

8889

Document type

Conference paper

Publisher

Springer

Topic

  • Computer Science

Keywords

  • Geometric decompositions
  • Minimum number rectangulation
  • Polyhedron
  • Matrix multiplication
  • Time complexity

Conference name

25th International Symposium on Algorithms and Computation (ISAAC), 2014

Conference date

2014-12-15 - 2014-12-17

Conference place

Jeonju, Korea, Republic of

Status

Published

ISBN/ISSN/Other

  • ISSN: 0302-9743
  • ISSN: 1611-3349
  • ISBN: 978-3-319-13074-3