23,598 research outputs found
Local Approximation Schemes for Ad Hoc and Sensor Networks
We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs
Minimum-Cost Coverage of Point Sets by Disks
We consider a class of geometric facility location problems in which the goal
is to determine a set X of disks given by their centers (t_j) and radii (r_j)
that cover a given set of demand points Y in the plane at the smallest possible
cost. We consider cost functions of the form sum_j f(r_j), where f(r)=r^alpha
is the cost of transmission to radius r. Special cases arise for alpha=1 (sum
of radii) and alpha=2 (total area); power consumption models in wireless
network design often use an exponent alpha>2. Different scenarios arise
according to possible restrictions on the transmission centers t_j, which may
be constrained to belong to a given discrete set or to lie on a line, etc. We
obtain several new results, including (a) exact and approximation algorithms
for selecting transmission points t_j on a given line in order to cover demand
points Y in the plane; (b) approximation algorithms (and an algebraic
intractability result) for selecting an optimal line on which to place
transmission points to cover Y; (c) a proof of NP-hardness for a discrete set
of transmission points in the plane and any fixed alpha>1; and (d) a
polynomial-time approximation scheme for the problem of computing a minimum
cost covering tour (MCCT), in which the total cost is a linear combination of
the transmission cost for the set of disks and the length of a tour/path that
connects the centers of the disks.Comment: 10 pages, 4 figures, Latex, to appear in ACM Symposium on
Computational Geometry 200
Constrained Signaling in Auction Design
We consider the problem of an auctioneer who faces the task of selling a good
(drawn from a known distribution) to a set of buyers, when the auctioneer does
not have the capacity to describe to the buyers the exact identity of the good
that he is selling. Instead, he must come up with a constrained signalling
scheme: a (non injective) mapping from goods to signals, that satisfies the
constraints of his setting. For example, the auctioneer may be able to
communicate only a bounded length message for each good, or he might be legally
constrained in how he can advertise the item being sold. Each candidate
signaling scheme induces an incomplete-information game among the buyers, and
the goal of the auctioneer is to choose the signaling scheme and accompanying
auction format that optimizes welfare. In this paper, we use techniques from
submodular function maximization and no-regret learning to give algorithms for
computing constrained signaling schemes for a variety of constrained signaling
problems
VoroCrust: Voronoi Meshing Without Clipping
Polyhedral meshes are increasingly becoming an attractive option with
particular advantages over traditional meshes for certain applications. What
has been missing is a robust polyhedral meshing algorithm that can handle broad
classes of domains exhibiting arbitrarily curved boundaries and sharp features.
In addition, the power of primal-dual mesh pairs, exemplified by
Voronoi-Delaunay meshes, has been recognized as an important ingredient in
numerous formulations. The VoroCrust algorithm is the first provably-correct
algorithm for conforming polyhedral Voronoi meshing for non-convex and
non-manifold domains with guarantees on the quality of both surface and volume
elements. A robust refinement process estimates a suitable sizing field that
enables the careful placement of Voronoi seeds across the surface circumventing
the need for clipping and avoiding its many drawbacks. The algorithm has the
flexibility of filling the interior by either structured or random samples,
while preserving all sharp features in the output mesh. We demonstrate the
capabilities of the algorithm on a variety of models and compare against
state-of-the-art polyhedral meshing methods based on clipped Voronoi cells
establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed
images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf.
Supplemental materials available on
https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd
Doppler peaks and all that: CMB anisotropies and what they can tell us
The power spectrum of fluctuations in the cosmic microwave background (CMB)
depends on most of the key cosmological parameters. Accurate future
measurements of this power spectrum might therefore allow us to determine h,
Omega, Omega_b, Lambda, n, T/S, etc, with hitherto unprecedented accuracy. In
these lecture notes, which are intended to be readable without much prior CMB
knowledge, I review the various physical processes that generate CMB
fluctuations, focusing on how changes in the parameters alters the shape of the
power spectrum. I also discuss foregrounds and real-world data analysis issues
and how these affect the accuracy with which the parameters can be measured.Comment: 40 pages, including 12 figures. Postscript. Latest version available
from http://astro.berkeley.edu/~max/power.html (faster from the US), from
http://www.mpa-garching.mpg.de/~max/power.html (faster from Europe) or from
[email protected]
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