Selection of a Large Sum-Free Subset in Polynomial Time

Abstract A set of E of integers is called sum-free if x + y ≠ z for all x , y , z ∈ E . Given a set A = { n 1 ,…, n N } of integers we show how to extract a sum-free subset E of A with | E | > N ⧸3. The algorithm requires polynomial time in the size of the input.