2,325 research outputs found
Many-to-One Boundary Labeling with Backbones
In this paper we study \emph{many-to-one boundary labeling with backbone
leaders}. In this new many-to-one model, a horizontal backbone reaches out of
each label into the feature-enclosing rectangle. Feature points that need to be
connected to this label are linked via vertical line segments to the backbone.
We present dynamic programming algorithms for label number and total leader
length minimization of crossing-free backbone labelings. When crossings are
allowed, we aim to obtain solutions with the minimum number of crossings. This
can be achieved efficiently in the case of fixed label order, however, in the
case of flexible label order we show that minimizing the number of leader
crossings is NP-hard.Comment: 23 pages, 10 figures, this is the full version of a paper that is
about to appear in GD'1
Rapid algorithm for identifying backbones in the two-dimensional percolation model
We present a rapid algorithm for identifying the current-carrying backbone in
the percolation model. It applies to general two-dimensional graphs with open
boundary conditions. Complemented by the modified Hoshen-Kopelman cluster
labeling algorithm, our algorithm identifies dangling parts using their local
properties. For planar graphs, it finds the backbone almost four times as fast
as Tarjan's depth-first-search algorithm, and uses the memory of the same size
as the modified Hoshen-Kopelman algorithm. Comparison with other algorithms for
backbone identification is addressed.Comment: 5 pages with 5 eps figures. RevTeX 3.1. Clarify the origin of the
hull-generating algorith
Models of discretized moduli spaces, cohomological field theories, and Gaussian means
We prove combinatorially the explicit relation between genus filtrated
-loop means of the Gaussian matrix model and terms of the genus expansion of
the Kontsevich--Penner matrix model (KPMM). The latter is the generating
function for volumes of discretized (open) moduli spaces
given by for
. This generating function therefore enjoys
the topological recursion, and we prove that it is simultaneously the
generating function for ancestor invariants of a cohomological field theory
thus enjoying the Givental decomposition. We use another Givental-type
decomposition obtained for this model by the second authors in 1995 in terms of
special times related to the discretisation of moduli spaces thus representing
its asymptotic expansion terms (and therefore those of the Gaussian means) as
finite sums over graphs weighted by lower-order monomials in times thus giving
another proof of (quasi)polynomiality of the discrete volumes. As an
application, we find the coefficients in the first subleading order for
in two ways: using the refined Harer--Zagier recursion and
by exploiting the above Givental-type transformation. We put forward the
conjecture that the above graph expansions can be used for probing the
reduction structure of the Delgne--Mumford compactification of moduli spaces of punctured Riemann surfaces.Comment: 36 pages in LaTex, 6 LaTex figure
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