47,974 research outputs found
Estimation of Buttiker-Landauer traversal time based on the visibility of transmission current
We present a proposal for the estimation of B\"uttiker-Landauer traversal
time based on the visibility of transmission current. We analyze the tunneling
phenomena with a time-dependent potential and obtain the time-dependent
transmission current. We found that the visibility is directly connected to the
traversal time. Furthermore, this result is valid not only for rectangular
potential barrier but also for general form of potential to which the WKB
approximation is applicable . We compared these results with the numerical
values obtained from the simulation of Nelson's quantum mechanics. Both of them
fit together and it shows our method is very effective to measure
experimentally the traversal time.Comment: 12 pages, REVTeX, including 7 eps figure
The Partial Visibility Representation Extension Problem
For a graph , a function is called a \emph{bar visibility
representation} of when for each vertex , is a
horizontal line segment (\emph{bar}) and iff there is an
unobstructed, vertical, -wide line of sight between and
. Graphs admitting such representations are well understood (via
simple characterizations) and recognizable in linear time. For a directed graph
, a bar visibility representation of , additionally, puts the bar
strictly below the bar for each directed edge of
. We study a generalization of the recognition problem where a function
defined on a subset of is given and the question is whether
there is a bar visibility representation of with for every . We show that for undirected graphs this problem
together with closely related problems are \NP-complete, but for certain cases
involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Compact Floor-Planning via Orderly Spanning Trees
Floor-planning is a fundamental step in VLSI chip design. Based upon the
concept of orderly spanning trees, we present a simple O(n)-time algorithm to
construct a floor-plan for any n-node plane triangulation. In comparison with
previous floor-planning algorithms in the literature, our solution is not only
simpler in the algorithm itself, but also produces floor-plans which require
fewer module types. An equally important aspect of our new algorithm lies in
its ability to fit the floor-plan area in a rectangle of size (n-1)x(2n+1)/3.
Lower bounds on the worst-case area for floor-planning any plane triangulation
are also provided in the paper.Comment: 13 pages, 5 figures, An early version of this work was presented at
9th International Symposium on Graph Drawing (GD 2001), Vienna, Austria,
September 2001. Accepted to Journal of Algorithms, 200
The Flip Diameter of Rectangulations and Convex Subdivisions
We study the configuration space of rectangulations and convex subdivisions
of points in the plane. It is shown that a sequence of
elementary flip and rotate operations can transform any rectangulation to any
other rectangulation on the same set of points. This bound is the best
possible for some point sets, while operations are sufficient and
necessary for others. Some of our bounds generalize to convex subdivisions of
points in the plane.Comment: 17 pages, 12 figures, an extended abstract has been presented at
LATIN 201
On Visibility Representations of Non-planar Graphs
A rectangle visibility representation (RVR) of a graph consists of an
assignment of axis-aligned rectangles to vertices such that for every edge
there exists a horizontal or vertical line of sight between the rectangles
assigned to its endpoints. Testing whether a graph has an RVR is known to be
NP-hard. In this paper, we study the problem of finding an RVR under the
assumption that an embedding in the plane of the input graph is fixed and we
are looking for an RVR that reflects this embedding. We show that in this case
the problem can be solved in polynomial time for general embedded graphs and in
linear time for 1-plane graphs (i.e., embedded graphs having at most one
crossing per edge). The linear time algorithm uses a precise list of forbidden
configurations, which extends the set known for straight-line drawings of
1-plane graphs. These forbidden configurations can be tested for in linear
time, and so in linear time we can test whether a 1-plane graph has an RVR and
either compute such a representation or report a negative witness. Finally, we
discuss some extensions of our study to the case when the embedding is not
fixed but the RVR can have at most one crossing per edge
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