Characterizing the Multi-Pass Streaming Complexity for Solving Boolean CSPs Exactly
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.
Streaming algorithms
Constraint Satisfaction Problems
Theory of computation~Streaming models
80:1-80:15
Regular Paper
Gillat
Kol
Gillat Kol
Princeton University, NJ, USA
Dmitry
Paramonov
Dmitry Paramonov
Princeton University, NJ, USA
Raghuvansh R.
Saxena
Raghuvansh R. Saxena
Microsoft, Cambridge, MA, USA
Huacheng
Yu
Huacheng Yu
Princeton University, NJ, USA
10.4230/LIPIcs.ITCS.2023.80
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