Results 1  10
of
21,639
Multilevel Algorithms for Wavefront Reduction
 SIAM J. SCIENTIFIC COMPUTING
, 2000
"... Multilevel algorithms are proposed for reordering sparse symmetric matrices to reduce the wavefront and profile. A graph representation of the matrix is used and two graph coarsening methods are investigated. A multilevel algorithm that uses a maximal independent vertex set for coarsening and the Sl ..."
Abstract

Cited by 20 (9 self)
 Add to MetaCart
Multilevel algorithms are proposed for reordering sparse symmetric matrices to reduce the wavefront and profile. A graph representation of the matrix is used and two graph coarsening methods are investigated. A multilevel algorithm that uses a maximal independent vertex set for coarsening
Multilevel Algorithms for Nonlinear Optimization
 IN OPTIMAL DESIGN AND CONTROL
, 1994
"... Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of th ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization startegy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations
Fast directional multilevel algorithms for . . .
, 2007
"... This paper introduces a new directional multilevel algorithm for solving Nbody or Npoint problems with highly oscillatory kernels. These systems often result from the boundary integral formulations of scattering problems and are difficult due to the oscillatory nature of the kernel and the nonu ..."
Abstract
 Add to MetaCart
This paper introduces a new directional multilevel algorithm for solving Nbody or Npoint problems with highly oscillatory kernels. These systems often result from the boundary integral formulations of scattering problems and are difficult due to the oscillatory nature of the kernel and the non
Multilevel algorithms for multiconstraint graph partitioning
 In Proceedings of Supercomputing
, 1998
"... ( kirk, karypis, kumar) @ cs.umn.edu ..."
Multilevel algorithms for . . . hypergraph partitioning
, 1999
"... Traditional hypergraph partitioning algorithms compute a bisection a graph such that the number of hyperedges that are cut by the partitioning is minimized and each partition has an equal number of vertices. The task of minimizing the cut can be considered as the objective and the requirement that t ..."
Abstract
 Add to MetaCart
such that the partitioning satisfies a balancing constraint associated with each weight, while attempting to minimize the cut. We present new multiconstraint hypergraph partitioning algorithms that are based on the multilevel partitioning paradigm. We experimentally evaluate the effectiveness of our multi
Multilevel Algorithm Exact solution
"... Finding a suitable compressed representation of largescale networks has been intensively studied in both practical and theoretical branches of data mining and network analysis [CS09, AM01, CKL+09, BV04, SBBA08]. In particular, the success of applying some of the recently proposed compression scheme ..."
Abstract
 Add to MetaCart
Finding a suitable compressed representation of largescale networks has been intensively studied in both practical and theoretical branches of data mining and network analysis [CS09, AM01, CKL+09, BV04, SBBA08]. In particular, the success of applying some of the recently proposed compression schemes [CKL+09, BV04, AD09] strongly depends on the “compressionfriendly ” arrangement of network nodes. Usually, the goal of these arrangements is to order the nodes such that the endpoints of network links (edges) are located as close as possible. Doing so leads to a more compact representation of links and allows a better performance of compression schemes and network element access operations. In [CKL+09], Chierichetti et al. propose to use ordering by the minimum logarithmic arrangement problem (MLogA), that minimizes the gap encodings of edges stretched between their endpoints. This is achieved by ordering the network nodes and assigning to them unique integer values (ids) such that the endpoints of a link will obtain close values. MLogA seeks a nearly optimal informationtheoretical compressed encoding size for all network links as it minimizes the total number of bits to spend for this purpose. The problem is NPhard. For example, instead of the popular network/matrix compressed row representation, which contains a sorted lists of neighbors per node, the following link gap encoding can be used. Compressed row format Gap format node number sorted neighbors sorted gaps 1 i,j,k,... i,ji,kj,... 2 p,q,r,... p,qp,rq,... Problem (GMLogA): Given a weighted graph G = (V,E), the goal of the linkweighted generalized minimum logarithmic arrangement problem is to minimize ij∈E wij lg pi(i) − pi(j)  over all permutations pi. Given node volumes, v, this is equivalent to the continuous version min pi ij∈E wij lg xi − xj  such that xi = vi
Parallel Multilevel Algorithms for Hypergraph Partitioning
, 2007
"... In this paper, we present parallel multilevel algorithms for the hypergraph partitioning problem. In particular, we describe schemes for parallel coarsening, parallel greedy kway refinement and parallel multiphase refinement. Using an asymptotic theoretical performance model, we derive the isoeffi ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
In this paper, we present parallel multilevel algorithms for the hypergraph partitioning problem. In particular, we describe schemes for parallel coarsening, parallel greedy kway refinement and parallel multiphase refinement. Using an asymptotic theoretical performance model, we derive
New Estimates for Multilevel Algorithms Including the VCycle
 MATH. COMP
, 1993
"... The purpose of this paper is to provide new estimates for certain multilevel algorithms. In particular, we are concerned with the simple additive multilevel algorithm given in [10] and the standard Vcycle algorithm with one smoothing step per grid. We shall prove that these algorithms have a unifo ..."
Abstract

Cited by 59 (5 self)
 Add to MetaCart
The purpose of this paper is to provide new estimates for certain multilevel algorithms. In particular, we are concerned with the simple additive multilevel algorithm given in [10] and the standard Vcycle algorithm with one smoothing step per grid. We shall prove that these algorithms have a
Results 1  10
of
21,639