70,616 research outputs found
On the editing distance of graphs
An edge-operation on a graph is defined to be either the deletion of an
existing edge or the addition of a nonexisting edge. Given a family of graphs
, the editing distance from to is the smallest
number of edge-operations needed to modify into a graph from .
In this paper, we fix a graph and consider , the set of
all graphs on vertices that have no induced copy of . We provide bounds
for the maximum over all -vertex graphs of the editing distance from
to , using an invariant we call the {\it binary chromatic
number} of the graph . We give asymptotically tight bounds for that distance
when is self-complementary and exact results for several small graphs
Stability of Reeb graphs under function perturbations: the case of closed curves
Reeb graphs provide a method for studying the shape of a manifold by encoding
the evolution and arrangement of level sets of a simple Morse function defined
on the manifold. Since their introduction in computer graphics they have been
gaining popularity as an effective tool for shape analysis and matching. In
this context one question deserving attention is whether Reeb graphs are robust
against function perturbations. Focusing on 1-dimensional manifolds, we define
an editing distance between Reeb graphs of curves, in terms of the cost
necessary to transform one graph into another. Our main result is that changes
in Morse functions induce smaller changes in the editing distance between Reeb
graphs of curves, implying stability of Reeb graphs under function
perturbations.Comment: 23 pages, 12 figure
On the Threshold of Intractability
We study the computational complexity of the graph modification problems
Threshold Editing and Chain Editing, adding and deleting as few edges as
possible to transform the input into a threshold (or chain) graph. In this
article, we show that both problems are NP-complete, resolving a conjecture by
Natanzon, Shamir, and Sharan (Discrete Applied Mathematics, 113(1):109--128,
2001). On the positive side, we show the problem admits a quadratic vertex
kernel. Furthermore, we give a subexponential time parameterized algorithm
solving Threshold Editing in time,
making it one of relatively few natural problems in this complexity class on
general graphs. These results are of broader interest to the field of social
network analysis, where recent work of Brandes (ISAAC, 2014) posits that the
minimum edit distance to a threshold graph gives a good measure of consistency
for node centralities. Finally, we show that all our positive results extend to
the related problem of Chain Editing, as well as the completion and deletion
variants of both problems
Multicolor and directed edit distance
The editing of a combinatorial object is the alteration of some of its
elements such that the resulting object satisfies a certain fixed property. The
edit problem for graphs, when the edges are added or deleted, was first studied
independently by the authors and K\'ezdy [J. Graph Theory (2008), 58(2),
123--138] and by Alon and Stav [Random Structures Algorithms (2008), 33(1),
87--104]. In this paper, a generalization of graph editing is considered for
multicolorings of the complete graph as well as for directed graphs.
Specifically, the number of edge-recolorings sufficient to be performed on any
edge-colored complete graph to satisfy a given hereditary property is
investigated. The theory for computing the edit distance is extended using
random structures and so-called types or colored homomorphisms of graphs.Comment: 25 page
Graph Edit Distance Reward: Learning to Edit Scene Graph
Scene Graph, as a vital tool to bridge the gap between language domain and
image domain, has been widely adopted in the cross-modality task like VQA. In
this paper, we propose a new method to edit the scene graph according to the
user instructions, which has never been explored. To be specific, in order to
learn editing scene graphs as the semantics given by texts, we propose a Graph
Edit Distance Reward, which is based on the Policy Gradient and Graph Matching
algorithm, to optimize neural symbolic model. In the context of text-editing
image retrieval, we validate the effectiveness of our method in CSS and CRIR
dataset. Besides, CRIR is a new synthetic dataset generated by us, which we
will publish it soon for future use.Comment: 14 pages, 6 figures, ECCV camera ready versio
Sequential Manipulation Planning on Scene Graph
We devise a 3D scene graph representation, contact graph+ (cg+), for
efficient sequential task planning. Augmented with predicate-like attributes,
this contact graph-based representation abstracts scene layouts with succinct
geometric information and valid robot-scene interactions. Goal configurations,
naturally specified on contact graphs, can be produced by a genetic algorithm
with a stochastic optimization method. A task plan is then initialized by
computing the Graph Editing Distance (GED) between the initial contact graphs
and the goal configurations, which generates graph edit operations
corresponding to possible robot actions. We finalize the task plan by imposing
constraints to regulate the temporal feasibility of graph edit operations,
ensuring valid task and motion correspondences. In a series of simulations and
experiments, robots successfully complete complex sequential object
rearrangement tasks that are difficult to specify using conventional planning
language like Planning Domain Definition Language (PDDL), demonstrating the
high feasibility and potential of robot sequential task planning on contact
graph.Comment: 8 pages, 6 figures. Accepted by IROS 202
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
Fast Parallel Fixed-Parameter Algorithms via Color Coding
Fixed-parameter algorithms have been successfully applied to solve numerous
difficult problems within acceptable time bounds on large inputs. However, most
fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no
use of the parallel hardware present in modern computers. We show that parallel
fixed-parameter algorithms do not only exist for numerous parameterized
problems from the literature -- including vertex cover, packing problems,
cluster editing, cutting vertices, finding embeddings, or finding matchings --
but that there are parallel algorithms working in \emph{constant} time or at
least in time \emph{depending only on the parameter} (and not on the size of
the input) for these problems. Phrased in terms of complexity classes, we place
numerous natural parameterized problems in parameterized versions of AC. On
a more technical level, we show how the \emph{color coding} method can be
implemented in constant time and apply it to embedding problems for graphs of
bounded tree-width or tree-depth and to model checking first-order formulas in
graphs of bounded degree
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