224,231 research outputs found
Analysis of dependence among size, rate and duration in internet flows
In this paper we examine rigorously the evidence for dependence among data
size, transfer rate and duration in Internet flows. We emphasize two
statistical approaches for studying dependence, including Pearson's correlation
coefficient and the extremal dependence analysis method. We apply these methods
to large data sets of packet traces from three networks. Our major results show
that Pearson's correlation coefficients between size and duration are much
smaller than one might expect. We also find that correlation coefficients
between size and rate are generally small and can be strongly affected by
applying thresholds to size or duration. Based on Transmission Control Protocol
connection startup mechanisms, we argue that thresholds on size should be more
useful than thresholds on duration in the analysis of correlations. Using
extremal dependence analysis, we draw a similar conclusion, finding remarkable
independence for extremal values of size and rate.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS268 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the phase transitions of graph coloring and independent sets
We study combinatorial indicators related to the characteristic phase
transitions associated with coloring a graph optimally and finding a maximum
independent set. In particular, we investigate the role of the acyclic
orientations of the graph in the hardness of finding the graph's chromatic
number and independence number. We provide empirical evidence that, along a
sequence of increasingly denser random graphs, the fraction of acyclic
orientations that are `shortest' peaks when the chromatic number increases, and
that such maxima tend to coincide with locally easiest instances of the
problem. Similar evidence is provided concerning the `widest' acyclic
orientations and the independence number
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