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Abstract:
Doerr and Fouz [\emphAsymptotically Optimal Randomized Rumor Spreading}, ICALP
2011] presented a new quasi-random PUSH algorithm for the rumor spreading
problem on complete graphs.
Their protocol is the first randomized PUSH protocol with an asymptotically
optimal running time.
This is achieved by equipping all nodes with the same lists, and by allowing
them to do a random restart after encountering an already informed node.
Here in this work, we show that
the same running time can be achieved if every second random restart is
replaced by a reversion of the direction in which the nodes follow their lists.
Put differently, our \emph{direction-reversing quasi-random rumor spreading
protocol with random restarts achieves the same running time as the hybrid
model by employing only (roughly) half the number of random choices.