1,130 research outputs found
Multiscale approach for the network compression-friendly ordering
We present a fast multiscale approach for the network minimum logarithmic
arrangement problem. This type of arrangement plays an important role in a
network compression and fast node/link access operations. The algorithm is of
linear complexity and exhibits good scalability which makes it practical and
attractive for using on large-scale instances. Its effectiveness is
demonstrated on a large set of real-life networks. These networks with
corresponding best-known minimization results are suggested as an open
benchmark for a research community to evaluate new methods for this problem
Layered Label Propagation: A MultiResolution Coordinate-Free Ordering for Compressing Social Networks
We continue the line of research on graph compression started with WebGraph,
but we move our focus to the compression of social networks in a proper sense
(e.g., LiveJournal): the approaches that have been used for a long time to
compress web graphs rely on a specific ordering of the nodes (lexicographical
URL ordering) whose extension to general social networks is not trivial. In
this paper, we propose a solution that mixes clusterings and orders, and devise
a new algorithm, called Layered Label Propagation, that builds on previous work
on scalable clustering and can be used to reorder very large graphs (billions
of nodes). Our implementation uses overdecomposition to perform aggressively on
multi-core architecture, making it possible to reorder graphs of more than 600
millions nodes in a few hours. Experiments performed on a wide array of web
graphs and social networks show that combining the order produced by the
proposed algorithm with the WebGraph compression framework provides a major
increase in compression with respect to all currently known techniques, both on
web graphs and on social networks. These improvements make it possible to
analyse in main memory significantly larger graphs
Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning
Multilevel partitioning methods that are inspired by principles of
multiscaling are the most powerful practical hypergraph partitioning solvers.
Hypergraph partitioning has many applications in disciplines ranging from
scientific computing to data science. In this paper we introduce the concept of
algebraic distance on hypergraphs and demonstrate its use as an algorithmic
component in the coarsening stage of multilevel hypergraph partitioning
solvers. The algebraic distance is a vertex distance measure that extends
hyperedge weights for capturing the local connectivity of vertices which is
critical for hypergraph coarsening schemes. The practical effectiveness of the
proposed measure and corresponding coarsening scheme is demonstrated through
extensive computational experiments on a diverse set of problems. Finally, we
propose a benchmark of hypergraph partitioning problems to compare the quality
of other solvers
Multilevel Methods for Sparsification and Linear Arrangement Problems on Networks
The computation of network properties such as diameter, centrality indices, and paths on networks may become a major bottleneck in the analysis of network if the network is large. Scalable approximation algorithms, heuristics and structure preserving network sparsification methods play an important role in modern network analysis. In the first part of this thesis, we develop a robust network sparsification method that enables filtering of either, so called, long- and short-range edges or both. Edges are first ranked by their algebraic distances and then sampled. Furthermore, we also combine this method with a multilevel framework to provide a multilevel sparsification framework that can control the sparsification process at different coarse-grained resolutions. Experimental results demonstrate an effectiveness of the proposed methods without significant loss in a quality of computed network properties. In the second part of the thesis, we introduce asymmetric coarsening schemes for multilevel algorithms developed for linear arrangement problems. Effectiveness of the set of coarse variables, and the corresponding interpolation matrix is the central problem in any multigrid algorithm. We are pushing the boundaries of fast maximum weighted matching algorithms for coarsening schemes on graphs by introducing novel ideas for asymmetric coupling between coarse and fine variables of the problem
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Multilevel Combinatorial Optimization Across Quantum Architectures
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the Post Moore\u27s law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave\u27s quantum annealer and IBM\u27s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size and observe results comparable to state-of-the-art solvers
Principal Patterns on Graphs: Discovering Coherent Structures in Datasets
Graphs are now ubiquitous in almost every field of research. Recently, new
research areas devoted to the analysis of graphs and data associated to their
vertices have emerged. Focusing on dynamical processes, we propose a fast,
robust and scalable framework for retrieving and analyzing recurring patterns
of activity on graphs. Our method relies on a novel type of multilayer graph
that encodes the spreading or propagation of events between successive time
steps. We demonstrate the versatility of our method by applying it on three
different real-world examples. Firstly, we study how rumor spreads on a social
network. Secondly, we reveal congestion patterns of pedestrians in a train
station. Finally, we show how patterns of audio playlists can be used in a
recommender system. In each example, relevant information previously hidden in
the data is extracted in a very efficient manner, emphasizing the scalability
of our method. With a parallel implementation scaling linearly with the size of
the dataset, our framework easily handles millions of nodes on a single
commodity server
Planar Graph Generation with Application to Water Distribution Networks
The study of network representations of physical, biological, and social phenomena can help us better understand their structure and functional dynamics as well as formulate predictive models of these phenomena. However, in some applications there is a deficiency in real-world data-sets for research purposes due to such reasons as the data sensitivity and high costs for data retrieval. Research related to water distribution networks often relies on synthetic data because the real-world is data is not publicly available due to the sensitivity towards theft and misuse. An important characteristic of water distribution systems is that they can be embedded in a plane, therefore to simulate these system we need realistic networks which are also planar. Currently available synthetic network generators can generate networks that exhibit realism but the planarity is not guaranteed. On the other hand, existing water network generators do not guarantee similarity with the input network and do not scale. In this thesis, we present a flexible method to generate realistic water distribution networks with optimized network parameters such as pipe and tank diameters, tank minimum and maximum levels, and pump sizes. Our model consists of three stages. First, we generate a realistic planar graph from a known water network using the multi-scale randomized edit- ing. Next, we add physical water network characteristics such as pumps, pipes, tanks, and reservoirs to the obtained topology to generate a realistic synthetic water distribution system that can be used for simulation. Finally, we optimize the operational parameters using EPANet simulation tool and multi-objective optimization solver to generate a network with maximum resilience and minimum cost
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