The average properties of the well-known Subset Sum Problem can be studied by means of its randomised version, where we are given a target value z, random variables X_1, …, X_n, and an error parameter ε > 0, and we seek a subset of the X_is whose sum approximates z up to error ε. In this setup, it has been shown that, under mild assumptions on the distribution of the random variables, a sample of size 𝒪(log(1/ε)) 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.
@InProceedings{dacunha_et_al:LIPIcs.ESA.2023.37, author = {Da Cunha, Arthur Carvalho Walraven and d'Amore, Francesco and Giroire, Fr\'{e}d\'{e}ric and Lesfari, Hicham and Natale, Emanuele and Viennot, Laurent}, title = {{Revisiting the Random Subset Sum Problem}}, booktitle = {31st Annual European Symposium on Algorithms (ESA 2023)}, pages = {37:1--37:11}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-295-2}, ISSN = {1868-8969}, year = {2023}, volume = {274}, editor = {G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.37}, URN = {urn:nbn:de:0030-drops-186905}, doi = {10.4230/LIPIcs.ESA.2023.37}, annote = {Keywords: Random subset sum, Randomised method, Subset-sum, Combinatorics} }
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