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Preprints, Working Papers, ... Year : 2022

Revisiting the Random Subset Sum problem


The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we seek a subset of the $X_i$'s whose sum approximates $z$ up to error $\varepsilon$. In this setup, it has been shown that, under mild assumptions on the distribution of the random variables, a sample of size $\mathcal{O}\left(\log (1/\varepsilon)\right)$ suffices to obtain, with high probability, approximations for all values in $[-1/2, 1/2]$. Recently, this result has been rediscovered outside the algorithms community, enabling meaningful progress in other fields. In this work we present an alternative proof for this theorem, with a more direct approach and resourcing to more elementary tools, in the hope of disseminating it even further.
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Dates and versions

hal-03654720 , version 1 (28-04-2022)
hal-03654720 , version 2 (30-03-2023)



Arthur da Cunha, Francesco d'Amore, Frédéric Giroire, Hicham Lesfari, Emanuele Natale, et al.. Revisiting the Random Subset Sum problem. 2022. ⟨hal-03654720v2⟩
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