Randomness vs. Time in Anonymous Networks [chapter]

Jochen Seidel, Jara Uitto, Roger Wattenhofer
2015 Lecture Notes in Computer Science  
In an anonymous network, symmetry breaking tasks can only be solved if randomization is available. But how many random bits are required to solve any such task? As it turns out, the answer to this question depends on the desired runtime of the algorithm. Since any randomized anonymous network algorithm can be decomposed into a randomized 2-hop coloring stage and a deterministic stage, we tackle the question by focusing on the randomized stage. We establish that for any reasonable target
more » ... f , there is a randomized 2-hop coloring scheme running in O(f (n)) time. Our coloring scheme allows to trade an increase in runtime by a factor of d for a decrease by the d th root in the random bit complexity.
doi:10.1007/978-3-662-48653-5_18 fatcat:i2tvb55hhvhb7fs6tu7plh42wy