OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
Gives a uniform randomized classical algorithm for worst-case Subset Sum in ordinary O(2^{0.49n}) word-RAM time on polynomial-bit inputs, where n counts the integers. The time bound holds on every execution and success probability is at least 2/3 on every input. Inputs may repeat positive integers; words have O(n+b) bits for maximum input bit length b.
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We give a uniform randomized classical algorithm for Subset Sum with bounded error and worst-case running time O(2^{0.49n}) on polynomial-bit inputs in a word-RAM model, where n is the number of input integers. The time bound holds on every random execution.
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We give a uniform classical randomized decision algorithm for worst-case Subset Sum. Under every fixed polynomial bound on input-integer bit length, it uses \mathop{poly}\nolimits (n)2^{n/2} time and ordinary O(2^{n/5}) writable words of O(n+b) bits, where b is the largest input bit length. Both resource bounds hold on every…
We give a uniform classical randomized decision algorithm for worst-case Subset Sum. Under every fixed polynomial bound on input-integer bit length, it uses \mathop{poly}\nolimits (n)2^{n/2} time and ordinary O(2^{n/5}) writable words of O(n+b) bits, where b is the largest input bit length. Both resource bounds hold on every execution. The error is one-sided: the algorithm always rejects unsolvable instances and accepts each solvable instance with probability at least 2/3.
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