Waiting Times for Ties in Random Competitions

TL;DR

This paper analyzes the timing of ties in random competitions among multiple teams, using martingale techniques, with applications to database rebalancing in storage engines.

Contribution

It introduces martingale-based methods to study tie occurrence times, linking theoretical probability to practical database rebalancing operations.

Findings

Derived bounds on tie occurrence times

Martingale constructions for stopping times

Applications to database rebalancing processes

Abstract

Multiple teams participate in a random competition. In each round the winner receives one point. We study the times until ties occur among teams. We construct martingales and supermartingales that enable us to prove the results regarding these stopping times. The problems studied in this paper are motivated by their applications to databases and their storage engines that are based on augmented balanced search trees. The ties in the competitions are related to the necessary rebalancing operations that have to be executed on the database.