40,013 research outputs found
Geodesic-Preserving Polygon Simplification
Polygons are a paramount data structure in computational geometry. While the
complexity of many algorithms on simple polygons or polygons with holes depends
on the size of the input polygon, the intrinsic complexity of the problems
these algorithms solve is often related to the reflex vertices of the polygon.
In this paper, we give an easy-to-describe linear-time method to replace an
input polygon by a polygon such that (1)
contains , (2) has its reflex
vertices at the same positions as , and (3) the number of vertices
of is linear in the number of reflex vertices. Since the
solutions of numerous problems on polygons (including shortest paths, geodesic
hulls, separating point sets, and Voronoi diagrams) are equivalent for both
and , our algorithm can be used as a preprocessing
step for several algorithms and makes their running time dependent on the
number of reflex vertices rather than on the size of
Space Shuffle: A Scalable, Flexible, and High-Bandwidth Data Center Network
Data center applications require the network to be scalable and
bandwidth-rich. Current data center network architectures often use rigid
topologies to increase network bandwidth. A major limitation is that they can
hardly support incremental network growth. Recent work proposes to use random
interconnects to provide growth flexibility. However routing on a random
topology suffers from control and data plane scalability problems, because
routing decisions require global information and forwarding state cannot be
aggregated. In this paper we design a novel flexible data center network
architecture, Space Shuffle (S2), which applies greedy routing on multiple ring
spaces to achieve high-throughput, scalability, and flexibility. The proposed
greedy routing protocol of S2 effectively exploits the path diversity of
densely connected topologies and enables key-based routing. Extensive
experimental studies show that S2 provides high bisectional bandwidth and
throughput, near-optimal routing path lengths, extremely small forwarding
state, fairness among concurrent data flows, and resiliency to network
failures
Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain
We study the computation of the diameter and radius under the rectilinear
link distance within a rectilinear polygonal domain of vertices and
holes. We introduce a \emph{graph of oriented distances} to encode the distance
between pairs of points of the domain. This helps us transform the problem so
that we can search through the candidates more efficiently. Our algorithm
computes both the diameter and the radius in time, where denotes the matrix
multiplication exponent and is the number of
edges of the graph of oriented distances. We also provide a faster algorithm
for computing the diameter that runs in time
Route Swarm: Wireless Network Optimization through Mobility
In this paper, we demonstrate a novel hybrid architecture for coordinating
networked robots in sensing and information routing applications. The proposed
INformation and Sensing driven PhysIcally REconfigurable robotic network
(INSPIRE), consists of a Physical Control Plane (PCP) which commands agent
position, and an Information Control Plane (ICP) which regulates information
flow towards communication/sensing objectives. We describe an instantiation
where a mobile robotic network is dynamically reconfigured to ensure high
quality routes between static wireless nodes, which act as source/destination
pairs for information flow. The ICP commands the robots towards evenly
distributed inter-flow allocations, with intra-flow configurations that
maximize route quality. The PCP then guides the robots via potential-based
control to reconfigure according to ICP commands. This formulation, deemed
Route Swarm, decouples information flow and physical control, generating a
feedback between routing and sensing needs and robotic configuration. We
demonstrate our propositions through simulation under a realistic wireless
network regime.Comment: 9 pages, 4 figures, submitted to the IEEE International Conference on
Intelligent Robots and Systems (IROS) 201
Visibility Graphs, Dismantlability, and the Cops and Robbers Game
We study versions of cop and robber pursuit-evasion games on the visibility
graphs of polygons, and inside polygons with straight and curved sides. Each
player has full information about the other player's location, players take
turns, and the robber is captured when the cop arrives at the same point as the
robber. In visibility graphs we show the cop can always win because visibility
graphs are dismantlable, which is interesting as one of the few results
relating visibility graphs to other known graph classes. We extend this to show
that the cop wins games in which players move along straight line segments
inside any polygon and, more generally, inside any simply connected planar
region with a reasonable boundary. Essentially, our problem is a type of
pursuit-evasion using the link metric rather than the Euclidean metric, and our
result provides an interesting class of infinite cop-win graphs.Comment: 23 page
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