118 research outputs found
A photonic chip based frequency discriminator for a high performance microwave photonic link
We report a high performance phase modulation direct detection microwave photonic link employing a photonic chip as a frequency discriminator. The photonic chip consists of five optical ring resonators (ORRs) which are fully programmable using thermo-optical tuning. In this discriminator a drop-port response of an ORR is cascaded with a through response of another ORR to yield a linear phase modulation (PM) to intensity modulation (IM) conversion. The balanced photonic link employing the PM to IM conversion exhibits high second-order and third-order input intercept points of + 46 dBm and + 36 dBm, respectively, which are simultaneously achieved at one bias point.\ud
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Kinetic Geodesic Voronoi Diagrams in a Simple Polygon
We study the geodesic Voronoi diagram of a set S of n linearly moving sites inside a static simple polygon P with m vertices. We identify all events where the structure of the Voronoi diagram changes, bound the number of such events, and then develop a kinetic data structure (KDS) that maintains the geodesic Voronoi diagram as the sites move. To this end, we first analyze how often a single bisector, defined by two sites, or a single Voronoi center, defined by three sites, can change. For both these structures we prove that the number of such changes is at most O(m³), and that this is tight in the worst case. Moreover, we develop compact, responsive, local, and efficient kinetic data structures for both structures. Our data structures use linear space and process a worst-case optimal number of events. Our bisector KDS handles each event in O(log m) time, and our Voronoi center handles each event in O(log² m) time. Both structures can be extended to efficiently support updating the movement of the sites as well. Using these data structures as building blocks we obtain a compact KDS for maintaining the full geodesic Voronoi diagram
Uncertain Curve Simplification
We study the problem of polygonal curve simplification under uncertainty,
where instead of a sequence of exact points, each uncertain point is
represented by a region, which contains the (unknown) true location of the
vertex. The regions we consider are disks, line segments, convex polygons, and
discrete sets of points. We are interested in finding the shortest subsequence
of uncertain points such that no matter what the true location of each
uncertain point is, the resulting polygonal curve is a valid simplification of
the original polygonal curve under the Hausdorff or the Fr\'echet distance. For
both these distance measures, we present polynomial-time algorithms for this
problem.Comment: 25 pages, 5 figure
Faster DBScan and HDBScan in Low-Dimensional Euclidean Spaces
We present a new algorithm for the widely used density-based clustering method DBScan. Our algorithm computes the DBScan-clustering in O(n log n) time in R^2, irrespective of the scale parameter eps, but assuming the second parameter MinPts is set to a fixed constant, as is the case in practice.
We also present an O(n log n) randomized algorithm for HDBScan in the plane---HDBScans is a hierarchical version of DBScan introduced recently---and we show how to compute an approximate version of HDBScan in near-linear time in any fixed dimension
On interference among moving sensors and related problems
We show that for any set of points moving along "simple" trajectories
(i.e., each coordinate is described with a polynomial of bounded degree) in
and any parameter , one can select a fixed non-empty
subset of the points of size , such that the Voronoi diagram of
this subset is "balanced" at any given time (i.e., it contains points
per cell). We also show that the bound is near optimal even for
the one dimensional case in which points move linearly in time. As
applications, we show that one can assign communication radii to the sensors of
a network of moving sensors so that at any given time their interference is
. We also show some results in kinetic approximate range
counting and kinetic discrepancy. In order to obtain these results, we extend
well-known results from -net theory to kinetic environments
Time-Space Trade-offs for Triangulating a Simple Polygon
An s-workspace algorithm is an algorithm that has read-only access to the values of the input, write-only access to the output, and only uses O(s) additional words of space. We give a randomized s-workspace algorithm for triangulating a simple polygon P of n vertices, for any s up to n. The algorithm runs in O(n^2/s+n(log s)log^5(n/s)) expected time using O(s) variables, for any s up to n. In particular, the algorithm runs in O(n^2/s) expected time for most values of s
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