Freestyle Dancing: Randomized Algorithms for Dynamic Storage Load-Balancing.

In this work, we study a challenging research problem that arises in minimizing the cost of storing customer data online for reliable accesses in a cloud. It is how to near-perfectly balance the remaining capacities of all disks across the cloud system while adding new file blocks so that the inevitable event of capacity expansion can be postponed as much as possible. The challenges of solving this problem are twofold. First, new file blocks are added to the cloud concurrently by many dispatchers (computing servers) that have no communication or coordination among themselves. Though each dispatcher is updated with information on disk occupancies, the update is infrequent and not synchronized. Second, for fault-tolerance purposes, a combinatorial constraint has to be satisfied in distributing the blocks of each new file across the cloud system. We propose a randomized algorithm, in which each dispatcher independently samples a blocks-to-disks assignment according to a probability distribution on a set of assignments conforming to the aforementioned combinatorial requirement. We show that this algorithm allows a cloud system to near-perfectly balance the remaining disk capacities as rapidly as theoretically possible, when starting from any unbalanced state that is correctable mathematically.