93,255 research outputs found
Combining spectral sequencing and parallel simulated annealing for the MinLA problem
In this paper we present and analyze new sequential and parallel
heuristics to approximate the Minimum Linear Arrangement problem
(MinLA). The heuristics consist in obtaining a first global solution
using Spectral Sequencing and improving it locally through Simulated
Annealing. In order to accelerate the annealing process, we present a
special neighborhood distribution that tends to favor moves with high
probability to be accepted. We show how to make use of this
neighborhood to parallelize the Metropolis stage on distributed memory
machines by mapping partitions of the input graph to processors and
performing moves concurrently. The paper reports the results obtained
with this new heuristic when applied to a set of large graphs,
including graphs arising from finite elements methods and graphs
arising from VLSI applications. Compared to other heuristics, the
measurements obtained show that the new heuristic improves the
solution quality, decreases the running time and offers an excellent
speedup when ran on a commodity network made of nine personal
computers.Postprint (published version
Persistent Homology Guided Force-Directed Graph Layouts
Graphs are commonly used to encode relationships among entities, yet their
abstractness makes them difficult to analyze. Node-link diagrams are popular
for drawing graphs, and force-directed layouts provide a flexible method for
node arrangements that use local relationships in an attempt to reveal the
global shape of the graph. However, clutter and overlap of unrelated structures
can lead to confusing graph visualizations. This paper leverages the persistent
homology features of an undirected graph as derived information for interactive
manipulation of force-directed layouts. We first discuss how to efficiently
extract 0-dimensional persistent homology features from both weighted and
unweighted undirected graphs. We then introduce the interactive persistence
barcode used to manipulate the force-directed graph layout. In particular, the
user adds and removes contracting and repulsing forces generated by the
persistent homology features, eventually selecting the set of persistent
homology features that most improve the layout. Finally, we demonstrate the
utility of our approach across a variety of synthetic and real datasets
The State-of-the-Art of Set Visualization
Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net
VLSI layouts and DNA physical mappings
We show that an important problem (-ICG) in computational biology is
equivalent to a colored version of a well-known graph layout problem (-CVS).Comment: 7 page
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