Approximation Algorithms for l0-Low Rank Approximation
نویسندگان
چکیده
For any column A:,i the best response vector is 1, so A:,i1 T − A 0 = 2 n − 1 = 2(1 − 1/n) OPTF 1 OPTF 1 = n Boolean l0-rank-1 Theorem 3. (Sublinear) Given A ∈ 0,1 m×n with column adjacency arrays and with row and column sums, we can compute w.h.p. in time O min A 0 +m + n, ψB −1 m + n log(mn) vectors u, v such that A − uv 0 ≤ 1 + O ψB OPTB . Theorem 4. (Exact) Given A ∈ 0,1 m×n with OPTB / A 0 ≤ 1/300, we can solves exactly the Boolean l0-rank-1 problem in time 2 O OPTB 1 / A 0 poly(mn).
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