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343
Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 140 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
Multilevel kway Hypergraph Partitioning
, 1999
"... In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on ..."
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Cited by 129 (7 self)
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In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on
Special Purpose Parallel Computing
 Lectures on Parallel Computation
, 1993
"... A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing ..."
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Cited by 77 (5 self)
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A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...
Spectral Partitioning: The More Eigenvectors, the Better
 PROC. ACM/IEEE DESIGN AUTOMATION CONF
, 1995
"... The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph's eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) which ..."
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Cited by 69 (3 self)
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The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph's eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) which are subsequently partitioned. Our main result shows that when all the eigenvectors are used, graph partitioning reduces to a new vector partitioning problem. This result implies that as many eigenvectors as are practically possible should be used to construct a solution. This philosophy isincontrast to that of the widelyused spectral bipartitioning (SB) heuristic (which uses a single eigenvector to construct a 2way partitioning) and several previous multiway partitioning heuristics [7][10][16][26][37] (which usek eigenvectors to construct a kway partitioning). Our result motivates a simple ordering heuristic that is a multipleeigenvector extension of SB. This heuristic not only signi cantly outperforms SB, but can also yield excellent multiway VLSI circuit partitionings as compared to [1] [10]. Our experiments suggest that the vector partitioning perspective opens the door to new and effective heuristics.
MemorySystem Design Considerations For DynamicallyScheduled Microprocessors
, 1997
"... MemorySystem Design Considerations for DynamicallyScheduled Microprocessors Keith Istvan Farkas Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 1997 Dynamicallyscheduled processors challenge hardware and software architects to develop designs ..."
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Cited by 69 (4 self)
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MemorySystem Design Considerations for DynamicallyScheduled Microprocessors Keith Istvan Farkas Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 1997 Dynamicallyscheduled processors challenge hardware and software architects to develop designs that balance hardware complexity and compiler technology against performance targets. This dissertation presents a first thorough look at some of the issues introduced by this hardware complexity. The focus of the investigation of these issues is the register file and the other components of the data memory system. These components are: the lockupfree data cache, the stream buffers, and the interface to the lower levels of the memory system. The investigation is based on software models. These models incorporate the features of a dynamicallyscheduled processor that affect the design of the datamemory components. The models represent a balance between accuracy and generality, and ar...
A TwoDimensional Data Distribution Method For Parallel Sparse MatrixVector Multiplication
 SIAM REVIEW
"... A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipar ..."
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Cited by 68 (9 self)
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A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipartitioning of the sparse matrix, each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros. The communication volume caused by the split is minimised. After the matrix partitioning, the input and output vectors are partitioned with the objective of minimising the maximum communication volume per processor. Experimental results of our implementation, Mondriaan, for a set of sparse test matrices show a reduction in communication compared to onedimensional methods, and in general a good balance in the communication work.
Multilevel hypergraph partitioning
 Applications in VLSI design, ACM/IEEE Design Automation Conference
, 1997
"... 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 ..."
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Cited by 64 (2 self)
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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 the partitions will be of the same size can be considered as the constraint. In this paper we extend the partitioning problem by incorporating an arbitrary number of balancing constraints. In our formulation, a vector of weights is assigned to each vertex, and the goal is to produce a bisection 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 multiconstraint partitioners on a variety of synthetically generated problems.
A Better Heuristic for Orthogonal Graph Drawings
 COMPUT. GEOM. THEORY APPL
, 1998
"... An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is ben ..."
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Cited by 61 (6 self)
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An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is bent at most twice. In particular for nonplanar and nonbiconnected planar graphs, this is a big improvement. The algorithm is very simple, easy to implement, and it handles both planar and nonplanar graphs at the same time.
HypergraphPartitioning Based Decomposition for Parallel SparseMatrix Vector Multiplication
 IEEE Trans. on Parallel and Distributed Computing
"... In this work, we show that the standard graphpartitioning based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrixvector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph mo ..."
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Cited by 61 (34 self)
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In this work, we show that the standard graphpartitioning based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrixvector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model. The proposed models reduce the decomposition problem to the wellknown hypergraph partitioning problem. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models. Experimental results on a wide range of realistic sparse test matrices confirm the validity of the proposed hypergraph models. In the decomposition of the test matrices, the hypergraph models using PaToH and hMeTiS result in up to 63% less communication volume (30%38% less on the average) than the graph model using MeTiS, while PaToH is only 1.32.3 times slower than MeTiS on the average. ...