Dominant resource fairness (DRF) is a popular mechanism for multi-resource allocation in cloud computing systems. In this paper, we consider the problem of multi-resource fair allocation with bounded number of tasks. We propose the lexicographically max-min normalized share (LMMNS) fair allocation mechanism, which is a natural generalization of DRF, and design a non-trivial optimal algorithm to
... [Show full abstract] find a LMMNS fair allocation, whose running time is linear in the number of users. Then, we prove that LMMNS satisfies envy-freeness and group strategy-proofness, and analyze the approximation ratios of LMMNS with some assumptions, by exploiting the properties of the optimal solution.