4,871 research outputs found
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
Dynamic Multilevel Graph Visualization
We adapt multilevel, force-directed graph layout techniques to visualizing
dynamic graphs in which vertices and edges are added and removed in an online
fashion (i.e., unpredictably). We maintain multiple levels of coarseness using
a dynamic, randomized coarsening algorithm. To ensure the vertices follow
smooth trajectories, we employ dynamics simulation techniques, treating the
vertices as point particles. We simulate fine and coarse levels of the graph
simultaneously, coupling the dynamics of adjacent levels. Projection from
coarser to finer levels is adaptive, with the projection determined by an
affine transformation that evolves alongside the graph layouts. The result is a
dynamic graph visualizer that quickly and smoothly adapts to changes in a
graph.Comment: 21 page
Magic-State Functional Units: Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures
Quantum computers have recently made great strides and are on a long-term
path towards useful fault-tolerant computation. A dominant overhead in
fault-tolerant quantum computation is the production of high-fidelity encoded
qubits, called magic states, which enable reliable error-corrected computation.
We present the first detailed designs of hardware functional units that
implement space-time optimized magic-state factories for surface code
error-corrected machines. Interactions among distant qubits require surface
code braids (physical pathways on chip) which must be routed. Magic-state
factories are circuits comprised of a complex set of braids that is more
difficult to route than quantum circuits considered in previous work [1]. This
paper explores the impact of scheduling techniques, such as gate reordering and
qubit renaming, and we propose two novel mapping techniques: braid repulsion
and dipole moment braid rotation. We combine these techniques with graph
partitioning and community detection algorithms, and further introduce a
stitching algorithm for mapping subgraphs onto a physical machine. Our results
show a factor of 5.64 reduction in space-time volume compared to the best-known
previous designs for magic-state factories.Comment: 13 pages, 10 figure
A Force-Directed Approach for Offline GPS Trajectory Map Matching
We present a novel algorithm to match GPS trajectories onto maps offline (in
batch mode) using techniques borrowed from the field of force-directed graph
drawing. We consider a simulated physical system where each GPS trajectory is
attracted or repelled by the underlying road network via electrical-like
forces. We let the system evolve under the action of these physical forces such
that individual trajectories are attracted towards candidate roads to obtain a
map matching path. Our approach has several advantages compared to traditional,
routing-based, algorithms for map matching, including the ability to account
for noise and to avoid large detours due to outliers in the data whilst taking
into account the underlying topological restrictions (such as one-way roads).
Our empirical evaluation using real GPS traces shows that our method produces
better map matching results compared to alternative offline map matching
algorithms on average, especially for routes in dense, urban areas.Comment: 10 pages, 12 figures, accepted version of article submitted to ACM
SIGSPATIAL 2018, Seattle, US
Maximizing the Total Resolution of Graphs
A major factor affecting the readability of a graph drawing is its
resolution. In the graph drawing literature, the resolution of a drawing is
either measured based on the angles formed by consecutive edges incident to a
common node (angular resolution) or by the angles formed at edge crossings
(crossing resolution). In this paper, we evaluate both by introducing the
notion of "total resolution", that is, the minimum of the angular and crossing
resolution. To the best of our knowledge, this is the first time where the
problem of maximizing the total resolution of a drawing is studied.
The main contribution of the paper consists of drawings of asymptotically
optimal total resolution for complete graphs (circular drawings) and for
complete bipartite graphs (2-layered drawings). In addition, we present and
experimentally evaluate a force-directed based algorithm that constructs
drawings of large total resolution
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