# Partition into c and 1-c

Let $$c\in(0,1/2]$$ be a constant. Given a set of positive integers with sum $$S$$, is there a partition into two subsets such that both subsets have sum at least $$cS$$?

If $$c=1/2$$, this is the famous partition problem which is NP-complete. What is known about the complexity for other values of $$c$$?

• It is NP-hard for every fixed constant $c$ with $0<c<1/2$. – Gamow Mar 24 at 17:42
• @Gamow Thanks. Could you please give a reference? – user52378 Mar 24 at 18:10
• @Gamow This is incorrect, according to Tom van der Zanden's answer on CS SE. – David Richerby Jun 19 at 15:07