License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.80
URN: urn:nbn:de:0030-drops-175837
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17583/
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Kol, Gillat ; Paramonov, Dmitry ; Saxena, Raghuvansh R. ; Yu, Huacheng

Characterizing the Multi-Pass Streaming Complexity for Solving Boolean CSPs Exactly

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LIPIcs-ITCS-2023-80.pdf (0.7 MB)

Abstract

We study boolean constraint satisfaction problems (CSPs) Max-CSP^f_n for all predicates f: {0,1}^k → {0,1}. In these problems, given an integer v and a list of constraints over n boolean variables, each obtained by applying f to a sequence of literals, we wish to decide if there is an assignment to the variables that satisfies at least v constraints. We consider these problems in the streaming model, where the algorithm makes a small number of passes over the list of constraints.
Our first and main result is the following complete characterization: For every predicate f, the streaming space complexity of the Max-CSP^f_n problem is Θ̃(n^deg(f)), where deg(f) is the degree of f when viewed as a multilinear polynomial. While the upper bound is obtained by a (very simple) one-pass streaming algorithm, our lower bound shows that a better space complexity is impossible even with constant-pass streaming algorithms.
Building on our techniques, we are also able to get an optimal Ω(n²) lower bound on the space complexity of constant-pass streaming algorithms for the well studied Max-CUT problem, even though it is not technically a Max-CSP^f_n problem as, e.g., negations of variables and repeated constraints are not allowed.

BibTeX - Entry

@InProceedings{kol_et_al:LIPIcs.ITCS.2023.80,
  author =	{Kol, Gillat and Paramonov, Dmitry and Saxena, Raghuvansh R. and Yu, Huacheng},
  title =	{{Characterizing the Multi-Pass Streaming Complexity for Solving Boolean CSPs Exactly}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{80:1--80:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17583},
  URN =		{urn:nbn:de:0030-drops-175837},
  doi =		{10.4230/LIPIcs.ITCS.2023.80},
  annote =	{Keywords: Streaming algorithms, Constraint Satisfaction Problems}
}

Keywords: Streaming algorithms, Constraint Satisfaction Problems
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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