37,099 research outputs found
Large scale probabilistic available bandwidth estimation
The common utilization-based definition of available bandwidth and many of
the existing tools to estimate it suffer from several important weaknesses: i)
most tools report a point estimate of average available bandwidth over a
measurement interval and do not provide a confidence interval; ii) the commonly
adopted models used to relate the available bandwidth metric to the measured
data are invalid in almost all practical scenarios; iii) existing tools do not
scale well and are not suited to the task of multi-path estimation in
large-scale networks; iv) almost all tools use ad-hoc techniques to address
measurement noise; and v) tools do not provide enough flexibility in terms of
accuracy, overhead, latency and reliability to adapt to the requirements of
various applications. In this paper we propose a new definition for available
bandwidth and a novel framework that addresses these issues. We define
probabilistic available bandwidth (PAB) as the largest input rate at which we
can send a traffic flow along a path while achieving, with specified
probability, an output rate that is almost as large as the input rate. PAB is
expressed directly in terms of the measurable output rate and includes
adjustable parameters that allow the user to adapt to different application
requirements. Our probabilistic framework to estimate network-wide
probabilistic available bandwidth is based on packet trains, Bayesian
inference, factor graphs and active sampling. We deploy our tool on the
PlanetLab network and our results show that we can obtain accurate estimates
with a much smaller measurement overhead compared to existing approaches.Comment: Submitted to Computer Network
On the threshold-width of graphs
The GG-width of a class of graphs GG is defined as follows. A graph G has
GG-width k if there are k independent sets N1,...,Nk in G such that G can be
embedded into a graph H in GG such that for every edge e in H which is not an
edge in G, there exists an i such that both endpoints of e are in Ni. For the
class TH of threshold graphs we show that TH-width is NP-complete and we
present fixed-parameter algorithms. We also show that for each k, graphs of
TH-width at most k are characterized by a finite collection of forbidden
induced subgraphs
Fast Scramblers, Horizons and Expander Graphs
We propose that local quantum systems defined on expander graphs provide a
simple microscopic model for thermalization on quantum horizons. Such systems
are automatically fast scramblers and are motivated from the membrane paradigm
by a conformal transformation to the so-called optical metric.Comment: 22 pages, 2 figures. Added further discussion in section 3. Added
reference
Triangle-free intersection graphs of line segments with large chromatic number
In the 1970s, Erdos asked whether the chromatic number of intersection graphs
of line segments in the plane is bounded by a function of their clique number.
We show the answer is no. Specifically, for each positive integer , we
construct a triangle-free family of line segments in the plane with chromatic
number greater than . Our construction disproves a conjecture of Scott that
graphs excluding induced subdivisions of any fixed graph have chromatic number
bounded by a function of their clique number.Comment: Small corrections, bibliography updat
Centroidal localization game
One important problem in a network is to locate an (invisible) moving entity
by using distance-detectors placed at strategical locations. For instance, the
metric dimension of a graph is the minimum number of detectors placed
in some vertices such that the vector
of the distances between the detectors and the entity's location
allows to uniquely determine . In a more realistic setting, instead
of getting the exact distance information, given devices placed in
, we get only relative distances between the entity's
location and the devices (for every , it is provided
whether , , or to ). The centroidal dimension of a
graph is the minimum number of devices required to locate the entity in
this setting.
We consider the natural generalization of the latter problem, where vertices
may be probed sequentially until the moving entity is located. At every turn, a
set of vertices is probed and then the relative distances
between the vertices and the current location of the entity are
given. If not located, the moving entity may move along one edge. Let be the minimum such that the entity is eventually located, whatever it
does, in the graph .
We prove that for every tree and give an upper bound
on in cartesian product of graphs and . Our main
result is that for any outerplanar graph . We then prove
that is bounded by the pathwidth of plus 1 and that the
optimization problem of determining is NP-hard in general graphs.
Finally, we show that approximating (up to any constant distance) the entity's
location in the Euclidean plane requires at most two vertices per turn
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