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• W4313351387 abstract "We revisit the maximum satisfiability problem (Max-SAT) in the data stream model. In this problem, the stream consists of m clauses that are disjunctions of literals drawn from n Boolean variables. The objective is to find an assignment to the variables that maximizes the number of satisfied clauses. Chou et al. (FOCS 2020) showed that $$varOmega (sqrt{n})$$ space is necessary to yield a $$sqrt{2}/2+varepsilon $$ approximation of the optimum value; they also presented an algorithm that yields a $$sqrt{2}/2-varepsilon $$ approximation of the optimum value using $$O(varepsilon ^{-2}log n)$$ space. In this paper, we focus not only on approximating the optimum value, but also on obtaining the corresponding Boolean assignment using sublinear o(mn) space. We present randomized single-pass algorithms that w.h.p. (W.h.p. denotes “with high probability”. Here, we consider $$1-1/{{,textrm{poly},}}(n)$$ or $$1-1/{{,textrm{poly},}}(m)$$ as high probability.) yield: Our ideas also extend to dynamic streams. On the other hand, we show that the streaming k-SAT problem that asks to decide whether one can satisfy all size-k input clauses must use $$varOmega (n^k)$$ space. We also consider the related minimum satisfiability problem ( $$text {Min-SAT} $$ ), introduced by Kohli et al. (SIAM J. Discrete Math. 1994), that asks to find an assignment that minimizes the number of satisfied clauses. For this problem, we give a $$tilde{O}(n^2/varepsilon ^2)$$ space algorithm, which is sublinear when $$m = omega (n)$$ , that yields an $$alpha +varepsilon $$ approximation where $$alpha $$ is the approximation guarantee of the offline algorithm. If each variable appears in at most f clauses, we show that a $$2sqrt{fn}$$ approximation using $$tilde{O}(n)$$ space is possible. Finally, for the Max-AND-SAT problem where clauses are conjunctions of literals, we show that any single-pass algorithm that approximates the optimal value up to a factor better than 1/2 with success probability at least 2/3 must use $$varOmega (mn)$$ space." @default.
• W4313351387 created "2023-01-06" @default.
• W4313351387 creator A5034746607 @default.
• W4313351387 date "2022-01-01" @default.
• W4313351387 modified "2023-10-16" @default.
• W4313351387 title "Revisiting Maximum Satisfiability and Related Problems in Data Streams" @default.
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• W4313351387 doi "https://doi.org/10.1007/978-3-031-22105-7_17" @default.
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