COMP 260: Advanced Algorithms
Tufts University
Prof. Lenore Cowen
Spring 2011
HW 3: due Thurs, February 17
1. Two little probability questions:
(a) From the formal definitions, show that if there is a Las Vegas
randomized algorithm that solves a problem, that this algorithm
can be converted to a Monte Carlo algorithm.
(b) Prove Chevychev’s inequality using Markov’s inequality
2. Consider the following alternative parallel MIS algorithm, where d(i)
denotes the degree of node i. Call a node unsatisfied if it was not
placed in the MIS and it does not yet have a neighbor in the MIS. The
algorithm proceeds in rounds, where in each round:
(a) unsatisfied processor i flips a 1 with probability 1/(4d(i)).
(b) If processor i flips a 1, and none of its neighbors of equal or greater
degree flips a 1, then processor i enters the MIS.
What is the expected number of rounds before this algorithm results
in an MIS? Give a careful probabilistic analysis.