Characterizing the Multi-Pass Streaming Complexity for Solving Boolean CSPs Exactly
| Autor: | Kol, Gillat, Paramonov, Dmitry, Saxena, Raghuvansh R., Yu, Huacheng |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
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| DOI: | 10.4230/lipics.itcs.2023.80 |
| Popis: | 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. LIPIcs, Vol. 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023), pages 80:1-80:15 |
| Databáze: | OpenAIRE |
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