Periodic Load Balancing on the N -Cycle: Analytical and Experimental Evaluation

We investigate the following very simple load-balancing algorithm on the N-cycle (N even) which we call Odd-Even Transposition Balancing (OETB). The edges of the cycle are partitioned into two matchings canonically. A matching defines a single step, the two matchings form a single round. Processors connected by an edge of the matching perfectly balance their loads, and, if there is an excess token, it is sent to the lower-numbered processor. The difference between the real process where the tokens are assumed integral and the idealized process where the tokens are assumed divisible can be expressed in terms of the local divergence [1]. We show that Odd-Even Transposition Balancing has a local divergence of N/2− 1. Combining this with previous results, this shows that after O(N log(KN)) rounds, any input sequence with initial imbalance K is perfectly balanced. Experiments are presented that show that the number of rounds necessary to perfectly balance a load sequence with imbalance K that has been obtained by pre-balancing a random sequence with much larger imbalance is significally larger than the average number of rounds necessary for balancing random sequences with imbalance K.