eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-02-26
48
61
10.4230/LIPIcs.STACS.2015.48
article
Subset Sum in the Absence of Concentration
Austrin, Per
Kaski, Petteri
Koivisto, Mikko
Nederlof, Jesper
We study the exact time complexity of the Subset Sum problem. Our focus is on instances that lack additive structure in the sense that the sums one can form from the subsets of the given integers are not strongly concentrated on any particular integer value. We present a randomized algorithm that runs in O(2^0.3399nB^4) time on instances with the property that no value can arise as a sum of more than B different subsets of the n given integers.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol030-stacs2015/LIPIcs.STACS.2015.48/LIPIcs.STACS.2015.48.pdf
subset sum
additive combinatorics
exponential-time algorithm
homomorphic hashing
Littlewood--Offord problem