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Conference 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 Carvalho Walraven da Cunha, Francesco d'Amore, Frédéric Giroire, Hicham Lesfari, Emanuele Natale, et al.. Revisiting the Random Subset Sum problem. 31st Annual European Symposium on Algorithms (ESA 2023), Sep 2023, Amsterdam, Netherlands. pp.37:1--37:11, ⟨10.4230/LIPIcs.ESA.2023.37⟩. ⟨hal-03654720v2⟩
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