59 research outputs found
Computing maximal cliques in link streams
A link stream is a collection of triplets indicating that an
interaction occurred between u and v at time t. We generalize the classical
notion of cliques in graphs to such link streams: for a given , a
-clique is a set of nodes and a time interval such that all pairs of
nodes in this set interact at least once during each sub-interval of duration
. We propose an algorithm to enumerate all maximal (in terms of nodes
or time interval) cliques of a link stream, and illustrate its practical
relevance on a real-world contact trace
Subgraph Matching Kernels for Attributed Graphs
We propose graph kernels based on subgraph matchings, i.e.
structure-preserving bijections between subgraphs. While recently proposed
kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al.,
2009) in general can not be applied to attributed graphs, our approach allows
to rate mappings of subgraphs by a flexible scoring scheme comparing vertex and
edge attributes by kernels. We show that subgraph matching kernels generalize
several known kernels. To compute the kernel we propose a graph-theoretical
algorithm inspired by a classical relation between common subgraphs of two
graphs and cliques in their product graph observed by Levi (1973). Encouraging
experimental results on a classification task of real-world graphs are
presented.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
Shadoks Approach to Convex Covering
We describe the heuristics used by the Shadoks team in the CG:SHOP 2023
Challenge. The Challenge consists of 206 instances, each being a polygon with
holes. The goal is to cover each instance polygon with a small number of convex
polygons. Our general strategy is the following. We find a big collection of
large (often maximal) convex polygons inside the instance polygon and then
solve several set cover problems to find a small subset of the collection that
covers the whole polygon.Comment: SoCG CG:SHOP 2023 Challeng
Communicability Graph and Community Structures in Complex Networks
We use the concept of the network communicability (Phys. Rev. E 77 (2008)
036111) to define communities in a complex network. The communities are defined
as the cliques of a communicability graph, which has the same set of nodes as
the complex network and links determined by the communicability function. Then,
the problem of finding the network communities is transformed to an all-clique
problem of the communicability graph. We discuss the efficiency of this
algorithm of community detection. In addition, we extend here the concept of
the communicability to account for the strength of the interactions between the
nodes by using the concept of inverse temperature of the network. Finally, we
develop an algorithm to manage the different degrees of overlapping between the
communities in a complex network. We then analyze the USA airport network, for
which we successfully detect two big communities of the eastern airports and of
the western/central airports as well as two bridging central communities. In
striking contrast, a well-known algorithm groups all but two of the continental
airports into one community.Comment: 36 pages, 5 figures, to appear in Applied Mathematics and Computatio
Shared-Memory Parallel Maximal Clique Enumeration
We present shared-memory parallel methods for Maximal Clique Enumeration
(MCE) from a graph. MCE is a fundamental and well-studied graph analytics task,
and is a widely used primitive for identifying dense structures in a graph. Due
to its computationally intensive nature, parallel methods are imperative for
dealing with large graphs. However, surprisingly, there do not yet exist
scalable and parallel methods for MCE on a shared-memory parallel machine. In
this work, we present efficient shared-memory parallel algorithms for MCE, with
the following properties: (1) the parallel algorithms are provably
work-efficient relative to a state-of-the-art sequential algorithm (2) the
algorithms have a provably small parallel depth, showing that they can scale to
a large number of processors, and (3) our implementations on a multicore
machine shows a good speedup and scaling behavior with increasing number of
cores, and are substantially faster than prior shared-memory parallel
algorithms for MCE.Comment: 10 pages, 3 figures, proceedings of the 25th IEEE International
Conference on. High Performance Computing, Data, and Analytics (HiPC), 201
Listing all maximal cliques in sparse graphs in near-optimal time
The degeneracy of an -vertex graph is the smallest number such that every subgraph of contains a vertex of degree at most . We show that there exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy. To achieve this result, we modify the classic Bron--Kerbosch algorithm and show that it runs in time . We also provide matching upper and lower bounds showing that the largest possible number of maximal cliques in an -vertex graph with degeneracy (when is a multiple of 3 and ) is . Therefore, our algorithm matches the worst-case output size of the problem whenever
Maximum Common Subgraph Isomorphism Algorithms
Maximum common subgraph (MCS) isomorphism algorithms play an important role in chemoinformatics by providing an effective mechanism for the alignment of pairs of chemical structures. This article discusses the various types of MCS that can be identified when two graphs are compared and reviews some of the algorithms that are available for this purpose, focusing on those that are, or may be, applicable to the matching of chemical graphs
A maximum common substructure-based algorithm for searching and predicting drug-like compounds
Motivation: The prediction of biologically active compounds is of great importance for high-throughput screening (HTS) approaches in drug discovery and chemical genomics. Many computational methods in this area focus on measuring the structural similarities between chemical structures. However, traditional similarity measures are often too rigid or consider only global similarities between structures. The maximum common substructure (MCS) approach provides a more promising and flexible alternative for predicting bioactive compounds
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