Separating Sublinear Time Computations by Approximate Diameter
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Approximating the distance to properties in bounded-degree and general sparse graphs
ACM Transactions on Algorithms (TALG)
Bounding Probability of Small Deviation: A Fourth Moment Approach
Mathematics of Operations Research
Throughput scaling of wireless networks with random connections
IEEE Transactions on Information Theory
Testing monotone continuous distributions on high-dimensional real cubes
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Property testing
Property testing
A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Nonnegative k-sums, fractional covers, and probability of small deviations
Journal of Combinatorial Theory Series B
On estimating the average degree
Proceedings of the 23rd international conference on World wide web
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We prove the following inequality: for every positive integer $n$ and every collection $X_1, \ldots, X_n$ of nonnegative independent random variables, each with expectation 1, the probability that their sum remains below $n+1$ is at least $\alpha 0$. Our proof produces a value of $\alpha = 1/13 \simeq 0.077$, but we conjecture that the inequality also holds with $\alpha = 1/e \simeq 0.368$.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 fewer 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.