2,890 research outputs found
Generating realistic scaled complex networks
Research on generative models is a central project in the emerging field of
network science, and it studies how statistical patterns found in real networks
could be generated by formal rules. Output from these generative models is then
the basis for designing and evaluating computational methods on networks, and
for verification and simulation studies. During the last two decades, a variety
of models has been proposed with an ultimate goal of achieving comprehensive
realism for the generated networks. In this study, we (a) introduce a new
generator, termed ReCoN; (b) explore how ReCoN and some existing models can be
fitted to an original network to produce a structurally similar replica, (c)
use ReCoN to produce networks much larger than the original exemplar, and
finally (d) discuss open problems and promising research directions. In a
comparative experimental study, we find that ReCoN is often superior to many
other state-of-the-art network generation methods. We argue that ReCoN is a
scalable and effective tool for modeling a given network while preserving
important properties at both micro- and macroscopic scales, and for scaling the
exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the
paper was presented at the 5th International Workshop on Complex Networks and
their Application
From Graph Theory to Network Science: The Natural Emergence of Hyperbolicity (Tutorial)
Network science is driven by the question which properties large real-world networks have and how we can exploit them algorithmically. In the past few years, hyperbolic graphs have emerged as a very promising model for scale-free networks. The connection between hyperbolic geometry and complex networks gives insights in both directions:
(1) Hyperbolic geometry forms the basis of a natural and explanatory model for real-world networks. Hyperbolic random graphs are obtained by choosing random points in the hyperbolic plane and connecting pairs of points that are geometrically close. The resulting networks share many structural properties for example with online social networks like Facebook or Twitter. They are thus well suited for algorithmic analyses in a more realistic setting.
(2) Starting with a real-world network, hyperbolic geometry is well-suited for metric embeddings. The vertices of a network can be mapped to points in this geometry, such that geometric distances are similar to graph distances. Such embeddings have a variety of algorithmic applications ranging from approximations based on efficient geometric algorithms to greedy routing solely using hyperbolic coordinates for navigation decisions
Communication Efficient Algorithms for Generating Massive Networks
Massive complex systems are prevalent throughout all of our lives, from various biological
systems as the human genome to technological networks such as Facebook or Twitter.
Rapid advances in technology allow us to gather more and more data that is connected to
these systems. Analyzing and extracting this huge amount of information is a crucial task
for a variety of scientific disciplines.
A common abstraction for handling complex systems are networks (graphs) made up of
entities and their relationships. For example, we can represent wireless ad hoc networks in
terms of nodes and their connections with each other.We then identify the nodes as vertices
and their connections as edges between the vertices. This abstraction allows us to develop
algorithms that are independent of the underlying domain.
Designing algorithms for massive networks is a challenging task that requires thorough
analysis and experimental evaluation. A major hurdle for this task is the scarcity of publicly
available large-scale datasets. To approach this issue, we can make use of network generators
[21]. These generators allow us to produce synthetic instances that exhibit properties
found in many real-world networks.
In this thesis we develop a set of novel graph generators that have a focus on scalability.
In particular, we cover the classic ErdËos-RĂ©nyi model, random geometric graphs and
random hyperbolic graphs. These models represent different real-world systems, from the
aforementioned wireless ad-hoc networks [40] to social networks [44].We ensure scalability
by making use of pseudorandomization via hash functions and redundant computations.
The resulting network generators are communication agnostic, i.e. they require no communication.
This allows us to generate massive instances of up to 243 vertices and 247 edges
in less than 22 minutes on 32:768 processors.
In addition to proving theoretical bounds for each generator, we perform an extensive
experimental evaluation. We cover both their sequential performance, as well as scaling
behavior.We are able to show that our algorithms are competitive to state-of-the-art implementations
found in network analysis libraries. Additionally, our generators exhibit near
optimal scaling behavior for large instances. Finally, we show that pseudorandomization
has little to no measurable impact on the quality of our generated instances
Generating Practical Random Hyperbolic Graphs in Near-Linear Time and with Sub-Linear Memory
Random graph models, originally conceived to study the structure of networks and the emergence of their properties, have become an indispensable tool for experimental algorithmics. Amongst them, hyperbolic random graphs form a well-accepted family, yielding realistic complex networks while being both mathematically and algorithmically tractable. We introduce two generators MemGen and HyperGen for the G_{alpha,C}(n) model, which distributes n random points within a hyperbolic plane and produces m=n*d/2 undirected edges for all point pairs close by; the expected average degree d and exponent 2*alpha+1 of the power-law degree distribution are controlled by alpha>1/2 and C. Both algorithms emit a stream of edges which they do not have to store. MemGen keeps O(n) items in internal memory and has a time complexity of O(n*log(log n) + m), which is optimal for networks with an average degree of d=Omega(log(log n)). For realistic values of d=o(n / log^{1/alpha}(n)), HyperGen reduces the memory footprint to O([n^{1-alpha}*d^alpha + log(n)]*log(n)).
In an experimental evaluation, we compare HyperGen with four generators among which it is consistently the fastest. For small d=10 we measure a speed-up of 4.0 compared to the fastest publicly available generator increasing to 29.6 for d=1000. On commodity hardware, HyperGen produces 3.7e8 edges per second for graphs with 1e6 < m < 1e12 and alpha=1, utilising less than 600MB of RAM. We demonstrate nearly linear scalability on an Intel Xeon Phi
Practical Minimum Cut Algorithms
The minimum cut problem for an undirected edge-weighted graph asks us to
divide its set of nodes into two blocks while minimizing the weight sum of the
cut edges. Here, we introduce a linear-time algorithm to compute near-minimum
cuts. Our algorithm is based on cluster contraction using label propagation and
Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both
sequential and shared-memory parallel implementations of our algorithm.
Extensive experiments on both real-world and generated instances show that our
algorithm finds the optimal cut on nearly all instances significantly faster
than other state-of-the-art algorithms while our error rate is lower than that
of other heuristic algorithms. In addition, our parallel algorithm shows good
scalability
Algorithms for Computing Maximum Cliques in Hyperbolic Random Graphs
In this paper, we study the maximum clique problem on hyperbolic random
graphs. A hyperbolic random graph is a mathematical model for analyzing
scale-free networks since it effectively explains the power-law degree
distribution of scale-free networks. We propose a simple algorithm for finding
a maximum clique in hyperbolic random graph. We first analyze the running time
of our algorithm theoretically. We can compute a maximum clique on a hyperbolic
random graph in expected time if a geometric
representation is given or in expected time if a
geometric representation is not given, where and denote the numbers of
vertices and edges of , respectively, and denotes a parameter
controlling the power-law exponent of the degree distribution of . Also, we
implemented and evaluated our algorithm empirically. Our algorithm outperforms
the previous algorithm [BFK18] practically and theoretically. Beyond the
hyperbolic random graphs, we have experiment on real-world networks. For most
of instances, we get large cliques close to the optimum solutions efficiently.Comment: Accepted in ESA 202
Algorithms for Computing Maximum Cliques in Hyperbolic Random Graphs
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of scale-free networks. We propose a simple algorithm for finding a maximum clique in hyperbolic random graph. We first analyze the running time of our algorithm theoretically. We can compute a maximum clique on a hyperbolic random graph G in O(m + n^{4.5(1-?)}) expected time if a geometric representation is given or in O(m + n^{6(1-?)}) expected time if a geometric representation is not given, where n and m denote the numbers of vertices and edges of G, respectively, and ? denotes a parameter controlling the power-law exponent of the degree distribution of G. Also, we implemented and evaluated our algorithm empirically. Our algorithm outperforms the previous algorithm [BFK18] practically and theoretically. Beyond the hyperbolic random graphs, we have experiment on real-world networks. For most of instances, we get large cliques close to the optimum solutions efficiently
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