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Fine Grained Space Complexity and the Linear Space Hypothesis (Preliminary Report)

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Book cover New Trends in Computer Technologies and Applications (ICS 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1723))

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Abstract

Theory of fine-grained time complexity has gained popularity in demonstrating tight bounds on the runtime required for solving target “tractable” problems under various complexity-theoretical hypotheses, including the strong exponential time hypothesis (SETH), the orthogonal vector problem (OVP), and the 3 sum problem (3SUM). Concerning space complexity limitations of tractable problems, as a natural analogy of SETH, the linear space hypothesis (LSH) was proposed in 2017 and it has been used to obtain better lower bounds on the space usage needed for solving several NL combinatorial problems. In further connection to LSH, we study the space complexity bounds of parameterized decision problems solvable in polylogarithmic time. In particular, we focus on a restricted OVP, which is called the 3-out-of-4 block orthogonal vector family problem (3/4-BOVF) parameterized by the number of matrix rows and, assuming LSH, we obtain a tight lower bound on the work space needed to solve 3/4-BOVF in polylogarithmic time. We also discuss space lower bounds of two more parameterized problems, called the 4 block matrix row majorization problem (4BMRM) parameterized by the number of matrix rows, and the 4 block vector summation problem (4BVSUM) parameterized by the number of set elements.

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Notes

  1. 1.

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Authors and Affiliations

  1. Faculty of Engineering, University of Fukui, 3-9-1 Bunkyo, Fukui, 910-8507, Japan

    Tomoyuki Yamakami

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  1. Tomoyuki Yamakami
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Correspondence to Tomoyuki Yamakami .

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Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Sun-Yuan Hsieh

  2. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  3. CNRS and University of Bordeaux, Talence, France

    Ralf Klasing

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

  5. National Taipei University of Business, Taoyuan, Taiwan

    Sheng-Lung Peng

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© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Yamakami, T. (2022). Fine Grained Space Complexity and the Linear Space Hypothesis (Preliminary Report). In: Hsieh, SY., Hung, LJ., Klasing, R., Lee, CW., Peng, SL. (eds) New Trends in Computer Technologies and Applications. ICS 2022. Communications in Computer and Information Science, vol 1723. Springer, Singapore. https://doi.org/10.1007/978-981-19-9582-8_16

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  • DOI: https://doi.org/10.1007/978-981-19-9582-8_16

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-9581-1

  • Online ISBN: 978-981-19-9582-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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