1,207,759 research outputs found
Geometric Interpretation of Theoretical Bounds for RSS-based Source Localization with Uncertain Anchor Positions
The Received Signal Strength based source localization can encounter severe
problems originating from uncertain information about the anchor positions in
practice. The anchor positions, although commonly assumed to be precisely known
prior to the source localization, are usually obtained using previous
estimation algorithm such as GPS. This previous estimation procedure produces
anchor positions with limited accuracy that result in degradations of the
source localization algorithm and topology uncertainty. We have recently
addressed the problem with a joint estimation framework that jointly estimates
the unknown source and uncertain anchors positions and derived the theoretical
limits of the framework. This paper extends the authors previous work on the
theoretical performance bounds of the joint localization framework with
appropriate geometric interpretation of the overall problem exploiting the
properties of semi-definiteness and symmetry of the Fisher Information Matrix
and the Cram{\`e}r-Rao Lower Bound and using Information and Error Ellipses,
respectively. The numerical results aim to illustrate and discuss the
usefulness of the geometric interpretation. They provide in-depth insight into
the geometrical properties of the joint localization problem underlining the
various possibilities for practical design of efficient localization
algorithms.Comment: 30 pages, 15 figure
Approximating Source Location and Star Survivable Network Problems
In Source Location (SL) problems the goal is to select a mini-mum cost source
set such that the connectivity (or flow) from
to any node is at least the demand of . In many SL problems
if , namely, the demand of nodes selected to is
completely satisfied. In a node-connectivity variant suggested recently by
Fukunaga, every node gets a "bonus" if it is selected to
. Fukunaga showed that for undirected graphs one can achieve ratio for his variant, where is the maximum demand. We
improve this by achieving ratio \min\{p^*\lnk,k\}\cdot O(\ln (k/q^*)) for a
more general version with node capacities, where is
the maximum bonus and is the minimum capacity. In
particular, for the most natural case considered by Fukunaga, we
improve the ratio from to . We also get ratio
for the edge-connectivity version, for which no ratio that depends on only
was known before. To derive these results, we consider a particular case of the
Survivable Network (SN) problem when all edges of positive cost form a star. We
give ratio for this variant, improving over the best
ratio known for the general case of Chuzhoy and Khanna
Algorithms for Constructing Overlay Networks For Live Streaming
We present a polynomial time approximation algorithm for constructing an
overlay multicast network for streaming live media events over the Internet.
The class of overlay networks constructed by our algorithm include networks
used by Akamai Technologies to deliver live media events to a global audience
with high fidelity. We construct networks consisting of three stages of nodes.
The nodes in the first stage are the entry points that act as sources for the
live streams. Each source forwards each of its streams to one or more nodes in
the second stage that are called reflectors. A reflector can split an incoming
stream into multiple identical outgoing streams, which are then sent on to
nodes in the third and final stage that act as sinks and are located in edge
networks near end-users. As the packets in a stream travel from one stage to
the next, some of them may be lost. A sink combines the packets from multiple
instances of the same stream (by reordering packets and discarding duplicates)
to form a single instance of the stream with minimal loss. Our primary
contribution is an algorithm that constructs an overlay network that provably
satisfies capacity and reliability constraints to within a constant factor of
optimal, and minimizes cost to within a logarithmic factor of optimal. Further
in the common case where only the transmission costs are minimized, we show
that our algorithm produces a solution that has cost within a factor of 2 of
optimal. We also implement our algorithm and evaluate it on realistic traces
derived from Akamai's live streaming network. Our empirical results show that
our algorithm can be used to efficiently construct large-scale overlay networks
in practice with near-optimal cost
Moving Walkways, Escalators, and Elevators
We study a simple geometric model of transportation facility that consists of
two points between which the travel speed is high. This elementary definition
can model shuttle services, tunnels, bridges, teleportation devices, escalators
or moving walkways. The travel time between a pair of points is defined as a
time distance, in such a way that a customer uses the transportation facility
only if it is helpful.
We give algorithms for finding the optimal location of such a transportation
facility, where optimality is defined with respect to the maximum travel time
between two points in a given set.Comment: 16 pages. Presented at XII Encuentros de Geometria Computacional,
Valladolid, Spai
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