Self-stabilizing Connected Components

Abstract

For the problem of computing the connected components of a graph, this paper considers the design of algorithms that are resilient to transient hardware faults, like bit flips. More specifically, it applies the technique of \emph{self-stabilization}. A system is self-stabilizing if, when starting from a valid or invalid state, it is guaranteed to reach a valid state after a finite number of steps. Therefore on a machine subject to a transient fault, a self-stabilizing algorithm could recover if that fault caused the system to enter an invalid state. We give a comprehensive analysis of the valid and invalid states during label propagation and derive algorithms to verify and correct the invalid state. The self-stabilizing label-propagation algorithm performs $\bigo{V \log V}$ additional computation and requires $\bigo{V}$ additional storage over its conventional counterpart (and, as such, does not increase asymptotic complexity over conventional \labelprop). When run against a battery of simulated fault injection tests, the self-stabilizing label propagation algorithm exhibits more resilient behavior than a triple modular redundancy (TMR) based fault-tolerant algorithm in $80\%$ of cases. From a performance perspective, it also outperforms TMR as it requires fewer iterations in total. Beyond the fault-tolerance properties of self-stabilizing label-propagation, we believe, they are useful from the theoretical perspective; and may have other use-cases.