1,165 research outputs found
L-Drawings of Directed Graphs
We introduce L-drawings, a novel paradigm for representing directed graphs
aiming at combining the readability features of orthogonal drawings with the
expressive power of matrix representations. In an L-drawing, vertices have
exclusive - and -coordinates and edges consist of two segments, one
exiting the source vertically and one entering the destination horizontally.
We study the problem of computing L-drawings using minimum ink. We prove its
NP-completeness and provide a heuristics based on a polynomial-time algorithm
that adds a vertex to a drawing using the minimum additional ink. We performed
an experimental analysis of the heuristics which confirms its effectiveness.Comment: 11 pages, 7 figure
Confluent Orthogonal Drawings of Syntax Diagrams
We provide a pipeline for generating syntax diagrams (also called railroad
diagrams) from context free grammars. Syntax diagrams are a graphical
representation of a context free language, which we formalize abstractly as a
set of mutually recursive nondeterministic finite automata and draw by
combining elements from the confluent drawing, layered drawing, and smooth
orthogonal drawing styles. Within our pipeline we introduce several heuristics
that modify the grammar but preserve the language, improving the aesthetics of
the final drawing.Comment: GD 201
How can we naturally order and organize graph Laplacian eigenvectors?
When attempting to develop wavelet transforms for graphs and networks, some
researchers have used graph Laplacian eigenvalues and eigenvectors in place of
the frequencies and complex exponentials in the Fourier theory for regular
lattices in the Euclidean domains. This viewpoint, however, has a fundamental
flaw: on a general graph, the Laplacian eigenvalues cannot be interpreted as
the frequencies of the corresponding eigenvectors. In this paper, we discuss
this important problem further and propose a new method to organize those
eigenvectors by defining and measuring "natural" distances between eigenvectors
using the Ramified Optimal Transport Theory followed by embedding them into a
low-dimensional Euclidean domain. We demonstrate its effectiveness using a
synthetic graph as well as a dendritic tree of a retinal ganglion cell of a
mouse
TopCom: Index for Shortest Distance Query in Directed Graph
Finding shortest distance between two vertices in a graph is an important
problem due to its numerous applications in diverse domains, including
geo-spatial databases, social network analysis, and information retrieval.
Classical algorithms (such as, Dijkstra) solve this problem in polynomial time,
but these algorithms cannot provide real-time response for a large number of
bursty queries on a large graph. So, indexing based solutions that pre-process
the graph for efficiently answering (exactly or approximately) a large number
of distance queries in real-time is becoming increasingly popular. Existing
solutions have varying performance in terms of index size, index building time,
query time, and accuracy. In this work, we propose T OP C OM , a novel
indexing-based solution for exactly answering distance queries. Our experiments
with two of the existing state-of-the-art methods (IS-Label and TreeMap) show
the superiority of T OP C OM over these two methods considering scalability and
query time. Besides, indexing of T OP C OM exploits the DAG (directed acyclic
graph) structure in the graph, which makes it significantly faster than the
existing methods if the SCCs (strongly connected component) of the input graph
are relatively small
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