17,492 research outputs found
Metric Dimension of Amalgamation of Graphs
A set of vertices resolves a graph if every vertex is uniquely
determined by its vector of distances to the vertices in . The metric
dimension of is the minimum cardinality of a resolving set of .
Let be a finite collection of graphs and each
has a fixed vertex or a fixed edge called a terminal
vertex or edge, respectively. The \emph{vertex-amalgamation} of , denoted by , is formed by taking all
the 's and identifying their terminal vertices. Similarly, the
\emph{edge-amalgamation} of , denoted by
, is formed by taking all the 's and identifying
their terminal edges.
Here we study the metric dimensions of vertex-amalgamation and
edge-amalgamation for finite collection of arbitrary graphs. We give lower and
upper bounds for the dimensions, show that the bounds are tight, and construct
infinitely many graphs for each possible value between the bounds.Comment: 9 pages, 2 figures, Seventh Czech-Slovak International Symposium on
Graph Theory, Combinatorics, Algorithms and Applications (CSGT2013), revised
version 21 December 201
A parallel genetic algorithm for the Steiner Problem in Networks
This paper presents a parallel genetic algorithm to the
Steiner Problem in Networks. Several previous papers
have proposed the adoption of GAs and others
metaheuristics to solve the SPN demonstrating the
validity of their approaches. This work differs from them
for two main reasons: the dimension and the
characteristics of the networks adopted in the experiments
and the aim from which it has been originated. The reason
that aimed this work was namely to build a comparison
term for validating deterministic and computationally
inexpensive algorithms which can be used in practical
engineering applications, such as the multicast
transmission in the Internet. On the other hand, the large
dimensions of our sample networks require the adoption
of a parallel implementation of the Steiner GA, which is
able to deal with such large problem instances
The space of ultrametric phylogenetic trees
The reliability of a phylogenetic inference method from genomic sequence data
is ensured by its statistical consistency. Bayesian inference methods produce a
sample of phylogenetic trees from the posterior distribution given sequence
data. Hence the question of statistical consistency of such methods is
equivalent to the consistency of the summary of the sample. More generally,
statistical consistency is ensured by the tree space used to analyse the
sample.
In this paper, we consider two standard parameterisations of phylogenetic
time-trees used in evolutionary models: inter-coalescent interval lengths and
absolute times of divergence events. For each of these parameterisations we
introduce a natural metric space on ultrametric phylogenetic trees. We compare
the introduced spaces with existing models of tree space and formulate several
formal requirements that a metric space on phylogenetic trees must possess in
order to be a satisfactory space for statistical analysis, and justify them. We
show that only a few known constructions of the space of phylogenetic trees
satisfy these requirements. However, our results suggest that these basic
requirements are not enough to distinguish between the two metric spaces we
introduce and that the choice between metric spaces requires additional
properties to be considered. Particularly, that the summary tree minimising the
square distance to the trees from the sample might be different for different
parameterisations. This suggests that further fundamental insight is needed
into the problem of statistical consistency of phylogenetic inference methods.Comment: Minor changes. This version has been published in JTB. 27 pages, 9
figure
On the strong partition dimension of graphs
We present a different way to obtain generators of metric spaces having the
property that the ``position'' of every element of the space is uniquely
determined by the distances from the elements of the generators. Specifically
we introduce a generator based on a partition of the metric space into sets of
elements. The sets of the partition will work as the new elements which will
uniquely determine the position of each single element of the space. A set
of vertices of a connected graph strongly resolves two different vertices
if either or
, where . An ordered vertex partition of
a graph is a strong resolving partition for if every two different
vertices of belonging to the same set of the partition are strongly
resolved by some set of . A strong resolving partition of minimum
cardinality is called a strong partition basis and its cardinality the strong
partition dimension. In this article we introduce the concepts of strong
resolving partition and strong partition dimension and we begin with the study
of its mathematical properties. We give some realizability results for this
parameter and we also obtain tight bounds and closed formulae for the strong
metric dimension of several graphs.Comment: 16 page
A Survey on Compiler Autotuning using Machine Learning
Since the mid-1990s, researchers have been trying to use machine-learning
based approaches to solve a number of different compiler optimization problems.
These techniques primarily enhance the quality of the obtained results and,
more importantly, make it feasible to tackle two main compiler optimization
problems: optimization selection (choosing which optimizations to apply) and
phase-ordering (choosing the order of applying optimizations). The compiler
optimization space continues to grow due to the advancement of applications,
increasing number of compiler optimizations, and new target architectures.
Generic optimization passes in compilers cannot fully leverage newly introduced
optimizations and, therefore, cannot keep up with the pace of increasing
options. This survey summarizes and classifies the recent advances in using
machine learning for the compiler optimization field, particularly on the two
major problems of (1) selecting the best optimizations and (2) the
phase-ordering of optimizations. The survey highlights the approaches taken so
far, the obtained results, the fine-grain classification among different
approaches and finally, the influential papers of the field.Comment: version 5.0 (updated on September 2018)- Preprint Version For our
Accepted Journal @ ACM CSUR 2018 (42 pages) - This survey will be updated
quarterly here (Send me your new published papers to be added in the
subsequent version) History: Received November 2016; Revised August 2017;
Revised February 2018; Accepted March 2018
Next Generation Cluster Editing
This work aims at improving the quality of structural variant prediction from
the mapped reads of a sequenced genome. We suggest a new model based on cluster
editing in weighted graphs and introduce a new heuristic algorithm that allows
to solve this problem quickly and with a good approximation on the huge graphs
that arise from biological datasets
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