Subset Sum in the Absence of Concentration

Authors Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof

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Per Austrin
Petteri Kaski
Mikko Koivisto
Jesper Nederlof

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Per Austrin, Petteri Kaski, Mikko Koivisto, and Jesper Nederlof. Subset Sum in the Absence of Concentration. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 48-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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.
  • subset sum
  • additive combinatorics
  • exponential-time algorithm
  • homomorphic hashing
  • Littlewood--Offord problem


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