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About this paper
Ce Jin, Xiao Mao
The authors give a deterministic algorithm for deciding whether a subset of n positive integers bounded by Δ reaches a target exactly. The method uses structured geometric representations to identify attainable interior sums and concentrates computation near the boundary. Its running time is O(n+Δ^{1+o(1)}), improving the prior general-case Õ(n+Δ^1.5) bound; this is asymptotic, leaves a subpolynomial gap to Õ(n+Δ).
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