Randomized Quasi Polynomial Algorithm for Subset-Sum Problems with At Most One Solution

08/29/2023

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by   Marius Costandin, et al.

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In this paper we study the Subset Sum Problem (SSP). Assuming the SSP has at most one solution, we provide a randomized quasi-polynomial algorithm which if the SSP has no solution, the algorithm always returns FALSE while if the SSP has a solution the algorithm returns TRUE with probability 1/2^log(n). This can be seen as two types of coins. One coin, when tossed always returns TAILS while the other also returns HEADS but with probability 1/2^log(n). Using the Law of Large Numbers one can identify the coin type and as such assert the existence of a solution to the SSP. The algorithm is developed in the more general framework of maximizing the distance to a given point over an intersection of balls.