Approximate majorization and fair online load balancing

This paper relates the notion of fairness in online routing and load balancing to vector majorization as developed by Hardy, Littlewood, and Polya 9]. We de ne -supermajorization as an approximate form of vector majorization, and show that this de nition generalizes and strengthens the pre x measure proposed by Kleinberg, Rabani and Tardos 11] as well as the popular notion of max-min fairness. The paper revisits the problem of online load-balancing for unrelated 1-1 machines from the viewpoint of fairness. We prove that a greedy approach is O(logn)-supermajorized by all other allocations, where n is the number of jobs. This means the greedy approach is globally O(logn)-fair. This may be constrasted with polynomial lower bounds presented in 7] for fair online routing. We also de ne a machine-centric view of fairness using the related concept of submajorization. We prove that the greedy online algorithm is globally O(logm)-balanced, where m is the number of machines.

• Type: Conference
• Year: 2001
• Where: SODA
• Authors: Ashish Goel, Adam Meyerson, Serge A. Plotkin
• Keywords: Algorithms, Greedy Approach, Online Routing, SODA 2001, Vector Majorization