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

by   Marius Costandin, et al.

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.


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