General Max-Min Fair Allocation

In the general max-min fair allocation, also known as Santa Claus problem, there are m players and n indivisible resources, each player has his/her own utilities for goal is to find an assignment that maximizes minimum total utility of resources assigned a player. We introduce over-estimation strategy help overcome challenges resource having different players. When all positive, we transform it machine covering problem \(\bigl (\frac{c}{1-\epsilon }\bigr )\)-approximate allocation in polynomial running time any fixed \(\epsilon \in (0,1)\), where c maximum ratio largest smallest resource. some zero, apply approximation algorithm Cheng Mao [9] restricted problem. It gives (1+3\hat{c}+O(\delta \hat{c}^2)\bigr \(\delta \(\hat{c}\) positive The ratios reasonable if small constants; example, when rate on 5-point scale.