13,434 research outputs found
Near-optimal adjacency labeling scheme for power-law graphs
An adjacency labeling scheme is a method that assigns labels to the vertices
of a graph such that adjacency between vertices can be inferred directly from
the assigned label, without using a centralized data structure. We devise
adjacency labeling schemes for the family of power-law graphs. This family that
has been used to model many types of networks, e.g. the Internet AS-level
graph. Furthermore, we prove an almost matching lower bound for this family. We
also provide an asymptotically near- optimal labeling scheme for sparse graphs.
Finally, we validate the efficiency of our labeling scheme by an experimental
evaluation using both synthetic data and real-world networks of up to hundreds
of thousands of vertices
A Generic Framework for Engineering Graph Canonization Algorithms
The state-of-the-art tools for practical graph canonization are all based on
the individualization-refinement paradigm, and their difference is primarily in
the choice of heuristics they include and in the actual tool implementation. It
is thus not possible to make a direct comparison of how individual algorithmic
ideas affect the performance on different graph classes.
We present an algorithmic software framework that facilitates implementation
of heuristics as independent extensions to a common core algorithm. It
therefore becomes easy to perform a detailed comparison of the performance and
behaviour of different algorithmic ideas. Implementations are provided of a
range of algorithms for tree traversal, target cell selection, and node
invariant, including choices from the literature and new variations. The
framework readily supports extraction and visualization of detailed data from
separate algorithm executions for subsequent analysis and development of new
heuristics.
Using collections of different graph classes we investigate the effect of
varying the selections of heuristics, often revealing exactly which individual
algorithmic choice is responsible for particularly good or bad performance. On
several benchmark collections, including a newly proposed class of difficult
instances, we additionally find that our implementation performs better than
the current state-of-the-art tools
A Survey on Graph Kernels
Graph kernels have become an established and widely-used technique for
solving classification tasks on graphs. This survey gives a comprehensive
overview of techniques for kernel-based graph classification developed in the
past 15 years. We describe and categorize graph kernels based on properties
inherent to their design, such as the nature of their extracted graph features,
their method of computation and their applicability to problems in practice. In
an extensive experimental evaluation, we study the classification accuracy of a
large suite of graph kernels on established benchmarks as well as new datasets.
We compare the performance of popular kernels with several baseline methods and
study the effect of applying a Gaussian RBF kernel to the metric induced by a
graph kernel. In doing so, we find that simple baselines become competitive
after this transformation on some datasets. Moreover, we study the extent to
which existing graph kernels agree in their predictions (and prediction errors)
and obtain a data-driven categorization of kernels as result. Finally, based on
our experimental results, we derive a practitioner's guide to kernel-based
graph classification
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