On the hardness of finding subsets with equal average

Authors:
Edith Elkind;James B. Orlin
Affiliations:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;MIT Sloan School of Management, USA
Venue:
Information Processing Letters
Year:
2013

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Abstract

We show that, given a set of positive integers, it is NP-complete to decide whether it contains two subsets with the same average. Our interest in this problem is motivated by questions in decision theory that are related to defining preferences on sets of objects given preferences over individual objects.