910 research outputs found
Fault-tolerant additive weighted geometric spanners
Let S be a set of n points and let w be a function that assigns non-negative
weights to points in S. The additive weighted distance d_w(p, q) between two
points p,q belonging to S is defined as w(p) + d(p, q) + w(q) if p \ne q and it
is zero if p = q. Here, d(p, q) denotes the (geodesic) Euclidean distance
between p and q. A graph G(S, E) is called a t-spanner for the additive
weighted set S of points if for any two points p and q in S the distance
between p and q in graph G is at most t.d_w(p, q) for a real number t > 1.
Here, d_w(p,q) is the additive weighted distance between p and q. For some
integer k \geq 1, a t-spanner G for the set S is a (k, t)-vertex fault-tolerant
additive weighted spanner, denoted with (k, t)-VFTAWS, if for any set S'
\subset S with cardinality at most k, the graph G \ S' is a t-spanner for the
points in S \ S'. For any given real number \epsilon > 0, we obtain the
following results:
- When the points in S belong to Euclidean space R^d, an algorithm to compute
a (k,(2 + \epsilon))-VFTAWS with O(kn) edges for the metric space (S, d_w).
Here, for any two points p, q \in S, d(p, q) is the Euclidean distance between
p and q in R^d.
- When the points in S belong to a simple polygon P, for the metric space (S,
d_w), one algorithm to compute a geodesic (k, (2 + \epsilon))-VFTAWS with
O(\frac{k n}{\epsilon^{2}}\lg{n}) edges and another algorithm to compute a
geodesic (k, (\sqrt{10} + \epsilon))-VFTAWS with O(kn(\lg{n})^2) edges. Here,
for any two points p, q \in S, d(p, q) is the geodesic Euclidean distance along
the shortest path between p and q in P.
- When the points in lie on a terrain T, an algorithm to compute a
geodesic (k, (2 + \epsilon))-VFTAWS with O(\frac{k n}{\epsilon^{2}}\lg{n})
edges.Comment: a few update
Recoverable DTN Routing based on a Relay of Cyclic Message-Ferries on a MSQ Network
An interrelation between a topological design of network and efficient
algorithm on it is important for its applications to communication or
transportation systems. In this paper, we propose a design principle for a
reliable routing in a store-carry-forward manner based on autonomously moving
message-ferries on a special structure of fractal-like network, which consists
of a self-similar tiling of equilateral triangles. As a collective adaptive
mechanism, the routing is realized by a relay of cyclic message-ferries
corresponded to a concatenation of the triangle cycles and using some good
properties of the network structure. It is recoverable for local accidents in
the hierarchical network structure. Moreover, the design principle is
theoretically supported with a calculation method for the optimal service rates
of message-ferries derived from a tandem queue model for stochastic processes
on a chain of edges in the network. These results obtained from a combination
of complex network science and computer science will be useful for developing a
resilient network system.Comment: 6 pages, 12 figures, The 3rd Workshop on the FoCAS(Fundamentals of
Collective Adaptive Systems) at The 9th IEEE International Conference on
SASO(Self-Adaptive and Self-Organizing systems), Boston, USA, Sept.21, 201
Controlling the sense of molecular rotation
We introduce a new scheme for controlling the sense of molecular rotation. By
varying the polarization and the delay between two ultrashort laser pulses, we
induce unidirectional molecular rotation, thereby forcing the molecules to
rotate clockwise/counterclockwise under field-free conditions. We show that
unidirectionally rotating molecules are confined to the plane defined by the
two polarization vectors of the pulses, which leads to a permanent anisotropy
in the molecular angular distribution. The latter may be useful for controlling
collisional cross-sections and optical and kinetic processes in molecular
gases. We discuss the application of this control scheme to individual
components within a molecular mixture in a selective manner.Comment: 21 pages, 10 figures, Submitted to the New Journal of Physics for the
"coherent control" special issu
Swirl-Inducing Ducts
This chapter examines the flow of swirling liquid in a duct. In many cases, circumferential velocity in the cross-section of a cylindrical duct is a remarkably linear function of radius up to the proximity of the duct wall. This is similar to the behaviour of a twisting solid shaft and the analogy leads to a solid body model for swirl flow in ducts. Helically profiled lobate duct walls provide a twisting torque, while wall friction in simple circular ducts causes swirl to decay. The liquid counterpart of the solid body is represented as a first-order system in downstream distance because of the way torque is transmitted by duct walls rather than by shaft stiffness as in the solid case. The effect of the inertia of the rotating and twisting cylinder is unchanged from its solid counterpart, and damping is related to the viscosity of the liquid acting over the annulus between the rotating liquid cylinder and the duct wall. The shear stress in the liquid is shown to be linearly related to the intensity of the swirl. The generation of swirl is briefly described with reference to lobate designs, their development of shape and helix
Undirected Connectivity of Sparse Yao Graphs
Given a finite set S of points in the plane and a real value d > 0, the
d-radius disk graph G^d contains all edges connecting pairs of points in S that
are within distance d of each other. For a given graph G with vertex set S, the
Yao subgraph Y_k[G] with integer parameter k > 0 contains, for each point p in
S, a shortest edge pq from G (if any) in each of the k sectors defined by k
equally-spaced rays with origin p. Motivated by communication issues in mobile
networks with directional antennas, we study the connectivity properties of
Y_k[G^d], for small values of k and d. In particular, we derive lower and upper
bounds on the minimum radius d that renders Y_k[G^d] connected, relative to the
unit radius assumed to render G^d connected. We show that d=sqrt(2) is
necessary and sufficient for the connectivity of Y_4[G^d]. We also show that,
for d =
2/sqrt(3), Y_3[G^d] is always connected. Finally, we show that Y_2[G^d] can be
disconnected, for any d >= 1.Comment: 7 pages, 11 figure
Robust Geometric Spanners
Highly connected and yet sparse graphs (such as expanders or graphs of high
treewidth) are fundamental, widely applicable and extensively studied
combinatorial objects. We initiate the study of such highly connected graphs
that are, in addition, geometric spanners. We define a property of spanners
called robustness. Informally, when one removes a few vertices from a robust
spanner, this harms only a small number of other vertices. We show that robust
spanners must have a superlinear number of edges, even in one dimension. On the
positive side, we give constructions, for any dimension, of robust spanners
with a near-linear number of edges.Comment: 18 pages, 8 figure
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