163,460 research outputs found
Compactifying Exchange Graphs I: Annuli and Tubes
We introduce the notion of an \emph{asymptotic triangulation} of the annulus.
We show that asymptotic triangulations can be mutated as the usual
triangulations and describe their exchange graph. Viewing asymptotic
triangulations as limits of triangulations under the action of the mapping
class group, we compactify the exchange graph of the triangulations of the
annulus. The cases of tubes are also considered.Comment: 14 page
Efficient Graph State Construction Under the Barrett and Kok Scheme
Recently Barrett and Kok (BK) proposed an elegant method for entangling
separated matter qubits. They outlined a strategy for using their entangling
operation (EO) to build graph states, the resource for one-way quantum
computing. However by viewing their EO as a graph fusion event, one perceives
that each successful event introduces an ideal redundant graph edge, which
growth strategies should exploit. For example, if each EO succeeds with
probability p=0.4 then a highly connected graph can be formed with an overhead
of only about ten EO attempts per graph edge. The BK scheme then becomes
competitive with the more elaborate entanglement procedures designed to permit
p to approach unity.Comment: 3 pages, 3 figures. Small refinement
A parent-centered radial layout algorithm for interactive graph visualization and animation
We have developed (1) a graph visualization system that allows users to
explore graphs by viewing them as a succession of spanning trees selected
interactively, (2) a radial graph layout algorithm, and (3) an animation
algorithm that generates meaningful visualizations and smooth transitions
between graphs while minimizing edge crossings during transitions and in static
layouts.
Our system is similar to the radial layout system of Yee et al. (2001), but
differs primarily in that each node is positioned on a coordinate system
centered on its own parent rather than on a single coordinate system for all
nodes. Our system is thus easy to define recursively and lends itself to
parallelization. It also guarantees that layouts have many nice properties,
such as: it guarantees certain edges never cross during an animation.
We compared the layouts and transitions produced by our algorithms to those
produced by Yee et al. Results from several experiments indicate that our
system produces fewer edge crossings during transitions between graph drawings,
and that the transitions more often involve changes in local scaling rather
than structure.
These findings suggest the system has promise as an interactive graph
exploration tool in a variety of settings
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