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- W2997474930 abstract "Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-varepsilon)$-approximation in time $tilde{O}(min{n/varepsilon, n+1/varepsilon^2})$ [Gens, Levner'78, Kellerer et al.'97]. In particular, a $(1-1/n)$-approximation can be computed in time $O(n^2)$. We establish a connection to the Min-Plus-Convolution problem, which is of particular interest in fine-grained complexity theory and can be solved naively in time $O(n^2)$. Our main result is that computing a $(1-1/n)$-approximation for Subset Sum is subquadratically equivalent to Min-Plus-Convolution. Thus, assuming the Min-Plus-Convolution conjecture from fine-grained complexity theory, there are no approximation schemes for Subset Sum with strongly subquadratic dependence on $n$ and $1/varepsilon$. In the other direction, our reduction allows us to transfer known lower order improvements from Min-Plus-Convolution to Subset Sum, which yields a mildly subquadratic approximation scheme. This adds the first approximation problem to the list of Min-Plus-Convolution-equivalent problems." @default.
- W2997474930 created "2020-01-10" @default.
- W2997474930 creator A5044394587 @default.
- W2997474930 date "2019-12-28" @default.
- W2997474930 modified "2023-09-27" @default.
- W2997474930 title "Approximating Subset Sum is equivalent to Min-Plus-Convolution." @default.
- W2997474930 hasPublicationYear "2019" @default.
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