Optimal information-dispersal for increasing the reliability of a distributed service

This paper investigates the (m,n) information dispersal scheme (IDS) used to support fault-tolerant distributed servers in a distributed system. In an (m,n)-IDS, a file M is broken into n pieces such that any m pieces collected suffice for reconstructing M. The reliability of an (m,n)-IDS is primarily determined by 3 important factors: n=information dispersal degree (IDD), n/m=information expansion ratio (IER), P_s=success-probability of acquiring a correct piece. It is difficult to determine the optimal IDS with the highest reliability from very many choices. Our analysis shows: several novel features of (m,n)-IDS which can help reduce the complexity of finding the optimal IDS with the highest reliability; that an IDS with a higher IER might not have a higher reliability, even when P_s→1. Based on the theorems given herein, we have developed a method that reduces the complexity for computing the highest reliability from, O(ν) [ν=number of servers] to O(1) when the `upper bound of the IER´=1, or O(ν<sup>2</sup>) to O(1) when the `upper bound of the IER´>1