1,765 research outputs found
Computing a rectilinear shortest path amid splinegons in plane
We reduce the problem of computing a rectilinear shortest path between two
given points s and t in the splinegonal domain \calS to the problem of
computing a rectilinear shortest path between two points in the polygonal
domain. As part of this, we define a polygonal domain \calP from \calS and
transform a rectilinear shortest path computed in \calP to a path between s and
t amid splinegon obstacles in \calS. When \calS comprises of h pairwise
disjoint splinegons with a total of n vertices, excluding the time to compute a
rectilinear shortest path amid polygons in \calP, our reduction algorithm takes
O(n + h \lg{n}) time. For the special case of \calS comprising of concave-in
splinegons, we have devised another algorithm in which the reduction procedure
does not rely on the structures used in the algorithm to compute a rectilinear
shortest path in polygonal domain. As part of these, we have characterized few
of the properties of rectilinear shortest paths amid splinegons which could be
of independent interest
Rock-salt SnS and SnSe: Native Topological Crystalline Insulators
Unlike time-reversal topological insulators, surface metallic states with
Dirac cone dispersion in the recently discovered topological crystalline
insulators (TCIs) are protected by crystal symmetry. To date, TCI behaviors
have been observed in SnTe and the related alloys PbSnSe/Te,
which incorporate heavy elements with large spin-orbit coupling (SOC). Here, by
combining first-principles and {\it ab initio} tight-binding calculations, we
report the formation of a TCI in the relatively lighter rock-salt SnS and SnSe.
This TCI is characterized by an even number of Dirac cones at the high-symmetry
(001), (110) and (111) surfaces, which are protected by the reflection symmetry
with respect to the (10) mirror plane. We find that both SnS and SnSe
have an intrinsically inverted band structure and the SOC is necessary only to
open the bulk band gap. The bulk band gap evolution upon volume expansion
reveals a topological transition from an ambient pressure TCI to a
topologically trivial insulator. Our results indicate that the SOC alone is not
sufficient to drive the topological transition.Comment: 5 pages, 5 figure
Electro-optic coupling of wide wavelength range in linear chirped-periodically poled lithium niobate and its applications
We theoretically investigate the electro-optic coupling in an optical superlattice of linear chirped-periodically poled lithium niobate. It is found that the electro-optic coupling in such optical superlattice can work in a wide wavelength range. Some of examples, with bandwidths of 20, 40, 80, 120nm, are demonstrated. The way to determine the electric field for perfect conversion between o- and e-ray and the method using apodized crystals of tanh profile to reduce the ripples are shown. As one of its applications, one kind of broadband Solc-type bandpass filter in optical communication range is proposed. (C) 2010 Optical Society of Americ
Capacitated Center Problems with Two-Sided Bounds and Outliers
In recent years, the capacitated center problems have attracted a lot of
research interest. Given a set of vertices , we want to find a subset of
vertices , called centers, such that the maximum cluster radius is
minimized. Moreover, each center in should satisfy some capacity
constraint, which could be an upper or lower bound on the number of vertices it
can serve. Capacitated -center problems with one-sided bounds (upper or
lower) have been well studied in previous work, and a constant factor
approximation was obtained.
We are the first to study the capacitated center problem with both capacity
lower and upper bounds (with or without outliers). We assume each vertex has a
uniform lower bound and a non-uniform upper bound. For the case of opening
exactly centers, we note that a generalization of a recent LP approach can
achieve constant factor approximation algorithms for our problems. Our main
contribution is a simple combinatorial algorithm for the case where there is no
cardinality constraint on the number of open centers. Our combinatorial
algorithm is simpler and achieves better constant approximation factor compared
to the LP approach
Optimal online and offline algorithms for robot-assisted restoration of barrier coverage
Cooperation between mobile robots and wireless sensor networks is a line of
research that is currently attracting a lot of attention. In this context, we
study the following problem of barrier coverage by stationary wireless sensors
that are assisted by a mobile robot with the capacity to move sensors. Assume
that sensors are initially arbitrarily distributed on a line segment
barrier. Each sensor is said to cover the portion of the barrier that
intersects with its sensing area. Owing to incorrect initial position, or the
death of some of the sensors, the barrier is not completely covered by the
sensors. We employ a mobile robot to move the sensors to final positions on the
barrier such that barrier coverage is guaranteed. We seek algorithms that
minimize the length of the robot's trajectory, since this allows the
restoration of barrier coverage as soon as possible. We give an optimal
linear-time offline algorithm that gives a minimum-length trajectory for a
robot that starts at one end of the barrier and achieves the restoration of
barrier coverage. We also study two different online models: one in which the
online robot does not know the length of the barrier in advance, and the other
in which the online robot knows the length of the barrier. For the case when
the online robot does not know the length of the barrier, we prove a tight
bound of on the competitive ratio, and we give a tight lower bound of
on the competitive ratio in the other case. Thus for each case we give an
optimal online algorithm.Comment: 20 page
Constraint Generation Algorithm for the Minimum Connectivity Inference Problem
Given a hypergraph , the Minimum Connectivity Inference problem asks for a
graph on the same vertex set as with the minimum number of edges such that
the subgraph induced by every hyperedge of is connected. This problem has
received a lot of attention these recent years, both from a theoretical and
practical perspective, leading to several implemented approximation, greedy and
heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear
Programming (MILP) formulations have been experimented, all representing
connectivity constraints by the means of graph flows. In this work, we
investigate the efficiency of a constraint generation algorithm, where we
iteratively add cut constraints to a simple ILP until a feasible (and optimal)
solution is found. It turns out that our method is faster than the previous
best flow-based MILP algorithm on random generated instances, which suggests
that a constraint generation approach might be also useful for other
optimization problems dealing with connectivity constraints. At last, we
present the results of an enumeration algorithm for the problem.Comment: 16 pages, 4 tables, 1 figur
Holographic Correlation Functions for Open Strings and Branes
In this paper, we compute holographically the two-point and three-point
functions of giant gravitons with open strings. We consider the maximal giant
graviton in and the string configurations corresponding to the ground
states of Z=0 and Y=0 open spin chain, and the spinning string in AdS
corresponding to the derivative type impurities in Y=0 or Z=0 open spin chain
as well. We treat the D-brane and open string contribution separately and find
the corresponding D3-brane and string configurations in bulk which connect the
composite operators at the AdS boundary. We apply a new prescription to
treat the string state contribution and find agreements for the two-point
functions. For the three-point functions of two giant gravitons with open
strings and one certain half-BPS chiral primary operator, we find that the
D-brane contributions to structure constant are always vanishing and the open
string contribution for the Y=0 ground state is in perfect match with the
prediction in the free field limit.Comment: 25 page
A fast algorithm to estimate generation capacity tripped by emergency control for transient stability of large power system
2008-2009 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe
Quantum mechanical analysis of nonlinear optical response of interacting graphene nanoflakes
We propose a distant-neighbor quantum-mechanical (DNQM) approach to study the linear and nonlinear optical properties of graphene nanoflakes (GNFs). In contrast to the widely used tight-binding description of the electronic states that considers only the nearest-neighbor coupling between the atoms, our approach is more accurate and general, as it captures the electron-core interactions between all atoms in the structure. Therefore, as we demonstrate, the DNQM approach enables the investigation of the optical coupling between two closely separated but chemically unbound GNFs. We also find that the optical response of GNFs depends crucially on their shape, size, and symmetry properties. Specifically, increasing the size of nanoflakes is found to shift their accommodated quantum plasmon oscillations to lower frequency. Importantly, we show that by embedding a cavity into GNFs, one can change their symmetry properties, tune their optical properties, or enable otherwise forbidden second-harmonic generation processes
A Technique for Obtaining True Approximations for -Center with Covering Constraints
There has been a recent surge of interest in incorporating fairness aspects
into classical clustering problems. Two recently introduced variants of the
-Center problem in this spirit are Colorful -Center, introduced by
Bandyapadhyay, Inamdar, Pai, and Varadarajan, and lottery models, such as the
Fair Robust -Center problem introduced by Harris, Pensyl, Srinivasan, and
Trinh. To address fairness aspects, these models, compared to traditional
-Center, include additional covering constraints. Prior approximation
results for these models require to relax some of the normally hard
constraints, like the number of centers to be opened or the involved covering
constraints, and therefore, only obtain constant-factor pseudo-approximations.
In this paper, we introduce a new approach to deal with such covering
constraints that leads to (true) approximations, including a -approximation
for Colorful -Center with constantly many colors---settling an open question
raised by Bandyapadhyay, Inamdar, Pai, and Varadarajan---and a
-approximation for Fair Robust -Center, for which the existence of a
(true) constant-factor approximation was also open. We complement our results
by showing that if one allows an unbounded number of colors, then Colorful
-Center admits no approximation algorithm with finite approximation
guarantee, assuming that . Moreover, under the
Exponential Time Hypothesis, the problem is inapproximable if the number of
colors grows faster than logarithmic in the size of the ground set
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