A Subspace Semidefinite Programming for Spectral Graph Partitioning

Oliveira, Suely; Stewart, David E.; Soma, Takako

doi:10.1007/3-540-46043-8_107

Cited by 1 publication

(2 citation statements)

References 20 publications

(26 reference statements)

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“…The SDP method for graph partitioning has been studied, e.g., in [49,106]. Oliveira [70] showed that a generalization of graph partitioning, where the vertices have preference values for belonging to a certain partition, can also be modeled as i i 1.5. Beyond traditional models a SDP.…”

Section: Semidefinite Programming For Graph Partitioningmentioning

confidence: 99%

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6. Partitioning and Load Balancing for Emerging Parallel Applications and Architectures

Devine¹,

Boman²,

Karypis³

2006

Parallel Processing for Scientific Computing

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Chapter 1. Partitioning and Load Balancing several different algorithms enable developers to easily compare methods to determine their effectiveness in applications [24, 26, 60]. Prior efforts have focused primarily on partitioning for homogeneous computing systems, where computing power and communication costs are roughly uniform. Wider acceptance of parallel computing has lead to an explosion of new parallel applications. Electronic circuit simulations, linear programming, materials modeling, crash simulations, and data mining are all adopting parallel computing to solve larger problems in less time. And the parallel architectures they use have evolved far from uniform arrays of multiprocessors. While homogeneous, dedicated parallel computers can offer the highest performance, their cost often is prohibitive. Instead, parallel computing is done on everything from networks of workstations to clusters of shared-memory processors to grid computers. These new applications and architectures have reached the limit of standard partitioners' effectiveness; they are driving development of new algorithms and software for partitioning. This paper surveys current research in partitioning and dynamic load balancing, with special emphasis on work presented at the 2004 SIAM Conference on Parallel Processing for Scientific Computing. "Traditional" load-balancing methods are summarized in §1.2. In §1.3, we describe several non-traditional applications along with effective partitioning strategies for them. Some non-traditional approaches to load balancing are described in §1.4. In §1.5, we describe partitioning goals that reach beyond typical load-balancing objectives. And in §1.6, we address load-balancing issues for non-traditional architectures.

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Section: Semidefinite Programming For Graph Partitioningmentioning

confidence: 99%

“…Subspace algorithms for SDP are analogous to Lanczos/Arnoldi or Davidson-type algorithms for eigenvalue problems. Recent work [70,71,72] indicates that such algorithms for SDP graph partitioning are much faster than full SDP solvers and are competitive with spectral partitioning.…”

Section: Semidefinite Programming For Graph Partitioningmentioning

confidence: 99%