A multilevel bilinear programming algorithm for the vertex separator problem

Hager, William W.; Hungerford, James T.; Safro, Ilya

doi:10.1007/s10589-017-9945-2

Cited by 20 publications

(23 citation statements)

References 29 publications

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“…One very promising direction is bridging the gaps between the theory and practice of multiscale computing and multilevel GP such as introducing nonlinear coarsening schemes. For example, a novel multilevel approach for the minimum vertex separator problem was recently proposed using the continuous bilinear quadratic program formulation [HHS14], and a hybrid of the geometric multigrid, and full approximation scheme for continuous problem was used for graph drawing, and VLSI placement problems [RSB10,CS03]. Development of more sophisticated coarsening schemes, edge ratings, and metrics of nodes' similarity that can be propagated throughout the hierarchies are among the future challenges for graph partitioning as well as any attempt of their rigorous analysis.…”

Section: Future Challengesmentioning

confidence: 99%

Recent Advances in Graph Partitioning

Buluç

Meyerhenke

Safro

et al. 2016

Lecture Notes in Computer Science

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Section: Future Challengesmentioning

confidence: 99%

Recent Advances in Graph Partitioning

Buluç

Meyerhenke

Safro

et al. 2016

Lecture Notes in Computer Science

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413

300

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“…The subproblem of optimizing community assignment of the subset is formulated by fixing community assignment for all vertices not in the subset (

i \notin X

) and encoding them into the optimization problem as boundary conditions. This is a commonly used technique in many heuristics . Denoting fixed assignments by

{\tilde{s}}_{j}

, the subproblem can be formulated as:

\begin{matrix} true \\ right Q_{s} & = & left \sum_{i > j false| i, j \in X} 2 B_{i j} s_{i} s_{j} + \sum_{i \in X} \sum_{j \notin X} 2 B_{i j} s_{i} {\tilde{s}}_{j} \\ = & left \sum_{i > j false| i, j \in X} 2 B_{i j} s_{i} s_{j} + \sum_{i \in X} C_{i} s_{i} \\ right where C_{i} & = & left \sum_{j \notin X} 2 B_{i j} {\tilde{s}}_{j} \end{matrix}

…”

Section: Quantum Local Searchmentioning

confidence: 99%

Network Community Detection on Small Quantum Computers

et al. 2019

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In recent years, a number of quantum computing devices with small numbers of qubits have become available. A hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size is presented. The proposed approach is applied to the network community detection problem. QLS is hardware-agnostic and easily extendable to new quantum computing devices as they become available. It is demonstrated to solve the 2-community detection problem on graphs of sizes of up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. The results herein demonstrate that QLS performs similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions.

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“…The main idea was based on the observation that the properties of real networks that should be preserved during generation are not only those measured at the finest resolution but also those that can be measured at the coarse resolutions. Multiscale generation leverages coarsening schemes used in highly-accurate multiscale solvers for combinatorial optimization such as linear arrangement, compression and partitioning [20][21][22][23][24]. In such coarsening schemes, nodes in a network are assigned into aggregates (or, typically, very small communities) which are themselves parts of larger aggregates and so on in a hierarchical manner.…”

Section: Editing Modelsmentioning

confidence: 99%

Multiscale planar graph generation

2019

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A network is a representation of a set of entities and the relationships between them. The network paradigm is often used to represent physical, biological, engineered and social systems [1]. Networks can help us better understand the structural and functional dynamics of these systems and formulate predictive models. However, collecting real-world network data often requires time and can be expensive. Also, for many applications, the sensitivity of real-world data towards theft and misuse further adds to the cost of protection and security of the data, which sharply limits its availability.The problem of data scarcity can be tackled by using synthetic data which can mimic both the properties and diversity of real world networks. Such synthetic data can be used for simulations, analysis, and performance/quality verification of algorithms -a crucial task in algorithm engineering. Synthetic network generation is one of the most important fields in network science from both theoretical and practical perspectives. We refer the reader for an in-depth discussion to recent reviews in [2,3].

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A multilevel bilinear programming algorithm for the vertex separator problem

Cited by 20 publications

References 29 publications

Recent Advances in Graph Partitioning

Recent Advances in Graph Partitioning

Network Community Detection on Small Quantum Computers

Multiscale planar graph generation

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