Given n different positive integers not greater than 2n-2, we prove that more than n^2/12 consecutive integers can be represented as the sum of half of the given numbers. This confirms a conjecture of Lev.
subset sum problem
Other combinatorial number theory (msc 11B75)
Walter de Gruyter
Integers; Electronic Journal of Combinatorial Number Theory
Spinoza prijs Lex Schrijver
This work was carried out under project PNA1-Spinoza Award
Networks and Optimization

Karolyi, G. (2009). Balanced subset sums of dense sets of integers. Integers; Electronic Journal of Combinatorial Number Theory, 9(A45), 591–603.