241 research outputs found
Counting and Enumerating Crossing-free Geometric Graphs
We describe a framework for counting and enumerating various types of
crossing-free geometric graphs on a planar point set. The framework generalizes
ideas of Alvarez and Seidel, who used them to count triangulations in time
where is the number of points. The main idea is to reduce the
problem of counting geometric graphs to counting source-sink paths in a
directed acyclic graph.
The following new results will emerge. The number of all crossing-free
geometric graphs can be computed in time for some .
The number of crossing-free convex partitions can be computed in time
. The number of crossing-free perfect matchings can be computed in
time . The number of convex subdivisions can be computed in time
. The number of crossing-free spanning trees can be computed in time
for some . The number of crossing-free spanning cycles
can be computed in time for some .
With the same bounds on the running time we can construct data structures
which allow fast enumeration of the respective classes. For example, after
time of preprocessing we can enumerate the set of all crossing-free
perfect matchings using polynomial time per enumerated object. For
crossing-free perfect matchings and convex partitions we further obtain
enumeration algorithms where the time delay for each (in particular, the first)
output is bounded by a polynomial in .
All described algorithms are comparatively simple, both in terms of their
analysis and implementation
A polynomial delay algorithm for the enumeration of bubbles with length constraints in directed graphs and its application to the detection of alternative splicing in RNA-seq data
We present a new algorithm for enumerating bubbles with length constraints in
directed graphs. This problem arises in transcriptomics, where the question is
to identify all alternative splicing events present in a sample of mRNAs
sequenced by RNA-seq. This is the first polynomial-delay algorithm for this
problem and we show that in practice, it is faster than previous approaches.
This enables us to deal with larger instances and therefore to discover novel
alternative splicing events, especially long ones, that were previously
overseen using existing methods.Comment: Peer-reviewed and presented as part of the 13th Workshop on
Algorithms in Bioinformatics (WABI2013
Efficient algorithms for enumerating maximal common subsequences of two strings
We propose efficient algorithms for enumerating maximal common subsequences
(MCSs) of two strings. Efficiency of the algorithms are estimated by the
preprocessing-time, space, and delay-time complexities. One algorithm prepares
a cubic-space data structure in cubic time to output each MCS in linear time.
This data structure can be used to search for particular MCSs satisfying some
condition without performing an explicit enumeration. Another prepares a
quadratic-space data structure in quadratic time to output each MCS in linear
time, and the other prepares a linear-space data structure in quadratic time to
output each MCS in linearithmic time.Comment: 23 pages, 5 Postscript figure
Efficient Generation of Stable Planar Cages for Chemistry
In this paper we describe an algorithm which generates all colored planar
maps with a good minimum sparsity from simple motifs and rules to connect them.
An implementation of this algorithm is available and is used by chemists who
want to quickly generate all sound molecules they can obtain by mixing some
basic components.Comment: 17 pages, 7 figures. Accepted at the 14th International Symposium on
Experimental Algorithms (SEA 2015
A Trichotomy for Regular Trail Queries
Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class T_tract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan et al. [Bagan et al., 2013]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice
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