Median bounds and their application
Journal of Algorithms
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
On Approximating the Average Distance Between Points
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
A sublinear-time approximation scheme for bin packing
Theoretical Computer Science
Approximating average parameters of graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Distance approximation in bounded-degree and general sparse graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We prove the following inequality: for every positive integer n and every collection X1,..., Xn of nonnegative independent random variables that each has expectation 1, the probability that their sum remains below n+1 is at least α 0. Our proof produces a value of α = 1/13 ≅ 0.077, but we conjecture that the inequality also holds with α = 1/e ≅ 0.368.As an example for the use of the new inequality, we consider the problem of estimating the average degree of a graph by querying the degrees of some of its vertices. We show the following threshold behavior: approximation factors above 2 require far less queries than approximation factors below 2. The new inequality is used in order to get tight (up to multiplicative constant factors) relations between the number of queries and the quality of the approximation. We show how the degree approximation algorithm can be used in order to quickly find those edges in a network that belong to many shortest paths.