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Partial Sums on the Ultra-Wide Word RAM

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Theory and Applications of Models of Computation (TAMC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12337))

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Abstract

We consider the classic partial sums problem on the ultra-wide word RAM model of computation. This model extends the classic w-bit word RAM model with special ultrawords of length \(w^2\) bits that support standard arithmetic and boolean operation and scattered memory access operations that can access w (non-contiguous) locations in memory. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures.

Our main result is a new in-place data structure for the partial sum problem that only stores a constant number of ultrawords in addition to the input and supports operations in doubly logarithmic time. This matches the best known time bounds for the problem (among polynomial space data structures) while improving the space from superlinear to a constant number of ultrawords. Our results are based on a simple and elegant in-place word RAM data structure, known as the Fenwick tree. Our main technical contribution is a new efficient parallel ultra-wide word RAM implementation of the Fenwick tree, which is likely of independent interest.

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Authors and Affiliations

  1. DTU Compute, Technical University of Denmark, Kgs. Lyngby, Denmark

    Philip Bille, Inge Li Gørtz & Frederik Rye Skjoldjensen

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  1. Philip Bille
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  2. Inge Li Gørtz
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  3. Frederik Rye Skjoldjensen
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Correspondence to Philip Bille .

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Editors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, USA

    Jianer Chen

  2. School of Computer Science and Engineering, Central South University, Changsha, China

    Qilong Feng

  3. Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY, USA

    Jinhui Xu

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Bille, P., Gørtz, I.L., Skjoldjensen, F.R. (2020). Partial Sums on the Ultra-Wide Word RAM. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham. https://doi.org/10.1007/978-3-030-59267-7_2

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  • DOI: https://doi.org/10.1007/978-3-030-59267-7_2

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