475 research outputs found
On the number of regular edge labelings
We prove that any irreducible triangulation on n vertices has O (4:6807n ) regular edge labeling,s and that there are irreducible triangulations on n vertices with (3:0426n ) regular edge labelings. Our upper bound relies on a novel application of Shearer's entropy lemma. As an example of the wider applicability of this technique, we also improve the upper bound on the number of 2-orientations of a quadrangulation to O (1:87n ). Keywords: Counting; Regular edge labeling; Shearer's entropy lemm
An Algorithmic Framework for Labeling Network Maps
Drawing network maps automatically comprises two challenging steps, namely
laying out the map and placing non-overlapping labels. In this paper we tackle
the problem of labeling an already existing network map considering the
application of metro maps. We present a flexible and versatile labeling model.
Despite its simplicity, we prove that it is NP-complete to label a single line
of the network. For a restricted variant of that model, we then introduce an
efficient algorithm that optimally labels a single line with respect to a given
weighting function. Based on that algorithm, we present a general and
sophisticated workflow for multiple metro lines, which is experimentally
evaluated on real-world metro maps.Comment: Full version of COCOON 2015 pape
Narrow sieves for parameterized paths and packings
We present randomized algorithms for some well-studied, hard combinatorial
problems: the k-path problem, the p-packing of q-sets problem, and the
q-dimensional p-matching problem. Our algorithms solve these problems with high
probability in time exponential only in the parameter (k, p, q) and using
polynomial space; the constant bases of the exponentials are significantly
smaller than in previous works. For example, for the k-path problem the
improvement is from 2 to 1.66. We also show how to detect if a d-regular graph
admits an edge coloring with colors in time within a polynomial factor of
O(2^{(d-1)n/2}).
Our techniques build upon and generalize some recently published ideas by I.
Koutis (ICALP 2009), R. Williams (IPL 2009), and A. Bj\"orklund (STACS 2010,
FOCS 2010)
Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models
We introduce a novel class of labeled directed acyclic graph (LDAG) models
for finite sets of discrete variables. LDAGs generalize earlier proposals for
allowing local structures in the conditional probability distribution of a
node, such that unrestricted label sets determine which edges can be deleted
from the underlying directed acyclic graph (DAG) for a given context. Several
properties of these models are derived, including a generalization of the
concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is
enabled by introducing an LDAG-based factorization of the Dirichlet prior for
the model parameters, such that the marginal likelihood can be calculated
analytically. In addition, we develop a novel prior distribution for the model
structures that can appropriately penalize a model for its labeling complexity.
A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill
climbing approach is used for illustrating the useful properties of LDAG models
for both real and synthetic data sets.Comment: 26 pages, 17 figure
On Optimal TCM Encoders
An asymptotically optimal trellis-coded modulation (TCM) encoder requires the
joint design of the encoder and the binary labeling of the constellation. Since
analytical approaches are unknown, the only available solution is to perform an
exhaustive search over the encoder and the labeling. For large constellation
sizes and/or many encoder states, however, an exhaustive search is unfeasible.
Traditional TCM designs overcome this problem by using a labeling that follows
the set-partitioning principle and by performing an exhaustive search over the
encoders. In this paper we study binary labelings for TCM and show how they can
be grouped into classes, which considerably reduces the search space in a joint
design. For 8-ary constellations, the number of different binary labelings that
must be tested is reduced from 8!=40320 to 240. For the particular case of an
8-ary pulse amplitude modulation constellation, this number is further reduced
to 120 and for 8-ary phase shift keying to only 30. An algorithm to generate
one labeling in each class is also introduced. Asymptotically optimal TCM
encoders are tabulated which are up to 0.3 dB better than the previously best
known encoders
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