Max-Min Allocation

Years and Authors of Summarized Original Work

• 2006; Bansal, Sviridenko

• 2007; Asadpour, Saberi

• 2008; Feige

• 2009; Chakrabarty, Chuzhoy, Khanna

Problem Definition

The max-min allocation problem has the following setting. There is a set A of m agents and a set I of n items. Each agent i ∈ A has utility $u_{\mathit{ij}} \in \mathbb{R}_{\geq 0}$ for item j ∈ I​. Given a subset of items $S \subseteq I$, the utility of this set to agent i is denoted as $u_{i}(S) :=\sum _{j\in S}u_{ij}$. The max-min allocation problem is to find an allocation of items to agents such that the minimum utility among the agents is maximized. That is, $\min _{i\in A}u_{i}(S_{i})$ is maximized, where $S_{i} \subseteq I$ is the set of items allocated to agent i and $S_{i} \cap S_{i^{{\prime}}} =\emptyset$.

The problem naturally arises as an approach to maximize fairness. Fairness is an important concept arising in numerous settings ranging from border disputes in political science to frequency allocations...