Randomized path coloring on binary trees

TL;DR: A polynomial-time $(5/3+\varepsilon)$-approximation algorithm is presented that selects a maximum-cardinality subset of the paths such that the selected paths are edge-disjoint.

TL;DR: This paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors.

TL;DR: This paper surveys recent advances in bandwidth allocation in tree-shaped WDM all-optical networks and gives the main ideas of deterministic greedy algorithms and their limitations and demonstrates how to achieve optimal and nearly-optimal bandwidth utilization in networks with wavelength converters using simple algorithms.

TL;DR: In this paper, a method and system for identifying optimal mapping of logical links to the physical topology of a network is provided, where the mapping options are correlated with the priority order of the network nodes.

Abstract: The classic text for understanding complex statistical probability An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivreLaplace theorem.

TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.

TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.

TL;DR: In this article, the Bienayme-Chebyshev inequality for random variables with finite rnean and variance was shown to hold for n independent, identically distributed random variables.