15,148 research outputs found
An Optimal Algorithm for Determining the Separation of Two Nonintersecting Simple Polygons
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-90-J-127
A scattering model of 1D quantum wire regular polygons
We calculate the quantum states of regular polygons made of 1D quantum wires
treating each polygon vertex as a scatterer. The vertex scattering matrix is
analytically obtained from the model of a circular bend of a given angle of a
2D nanowire. In the single mode limit the spectrum is classified in doublets of
vanishing circulation, twofold split by the small vertex reflection, and
singlets with circulation degeneracy. Simple analytic expressions of the energy
eigenvalues are given. It is shown how each polygon is characterized by a
specific spectrum.Comment: 8 pages, 5 figure
Complexity of Interlocking Polyominoes
Polyominoes are a subset of polygons which can be constructed from
integer-length squares fused at their edges. A system of polygons P is
interlocked if no subset of the polygons in P can be removed arbitrarily far
away from the rest. It is already known that polyominoes with four or fewer
squares cannot interlock. It is also known that determining the interlockedness
of polyominoes with an arbitrary number of squares is PSPACE hard. Here, we
prove that a system of polyominoes with five or fewer squares cannot interlock,
and that determining interlockedness of a system of polyominoes including
hexominoes (polyominoes with six squares) or larger polyominoes is PSPACE hard.Comment: 18 pages, 15 figure
Engineering Art Galleries
The Art Gallery Problem is one of the most well-known problems in
Computational Geometry, with a rich history in the study of algorithms,
complexity, and variants. Recently there has been a surge in experimental work
on the problem. In this survey, we describe this work, show the chronology of
developments, and compare current algorithms, including two unpublished
versions, in an exhaustive experiment. Furthermore, we show what core
algorithmic ingredients have led to recent successes
Computing largest circles separating two sets of segments
A circle separates two planar sets if it encloses one of the sets and its
open interior disk does not meet the other set. A separating circle is a
largest one if it cannot be locally increased while still separating the two
given sets. An Theta(n log n) optimal algorithm is proposed to find all largest
circles separating two given sets of line segments when line segments are
allowed to meet only at their endpoints. In the general case, when line
segments may intersect times, our algorithm can be adapted to
work in O(n alpha(n) log n) time and O(n \alpha(n)) space, where alpha(n)
represents the extremely slowly growing inverse of the Ackermann function.Comment: 14 pages, 3 figures, abstract presented at 8th Canadian Conference on
Computational Geometry, 199
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