Restricted max-min fair allocations with inclusion-free intervals

Abstract

We consider the restricted assignment version of the problem of fairly allocating a set of m indivisible items to n agents (also known as the Santa Claus problem). We study the variant where every item has some non-negative value and it can be assigned to an interval of players (i.e. to a set of consecutive players). Moreover, intervals are inclusion free. The goal is to distribute the items to the players and fair allocations in this context are those maximizing the minimum utility received by any agent. When every item can be assigned to any player a PTAS is known [Woe97]. We present a 1/2-approximation algorithm for the addressed more general variant with inclusion-free intervals. © 2012 Springer-Verlag.