Journal ArticleDOI
An r-Dimensional Quadratic Placement Algorithm
TLDR
In this paper, the problem of placing n connected points (or nodes) in r-dimensional Euclidean space is given, and the criterion for optimality is minimizing a weighted sum of squared distances between the points subject to quadratic constraints of the form X′X = 1, for each of the r unknown coordinate vectors.Abstract:
In this paper the solution to the problem of placing n connected points (or nodes) in r-dimensional Euclidean space is given. The criterion for optimality is minimizing a weighted sum of squared distances between the points subject to quadratic constraints of the form X′X = 1, for each of the r unknown coordinate vectors. It is proved that the problem reduces to the minimization of a sum or r positive semi-definite quadratic forms which, under the quadratic constraints, reduces to the problem of finding r eigenvectors of a special “disconnection” matrix. It is shown, by example, how this can serve as a basis for cluster identification.read more
Citations
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Journal ArticleDOI
Complex networks: Structure and dynamics
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
Proceedings ArticleDOI
Co-clustering documents and words using bipartite spectral graph partitioning
TL;DR: A new spectral co-clustering algorithm is used that uses the second left and right singular vectors of an appropriately scaled word-document matrix to yield good bipartitionings and it can be shown that the singular vectors solve a real relaxation to the NP-complete graph bipartitionsing problem.
Journal ArticleDOI
Fast spectral methods for ratio cut partitioning and clustering
L. Hagen,Andrew B. Kahng +1 more
TL;DR: It is shown that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost.
Journal ArticleDOI
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
TL;DR: This paper develops a fast high-quality multilevel algorithm that directly optimizes various weighted graph clustering objectives, such as the popular ratio cut, normalized cut, and ratio association criteria, and demonstrates that the algorithm is applicable to large-scale clustering tasks such as image segmentation, social network analysis, and gene network analysis.
Book
Algorithms for VLSI Physical Design Automation
TL;DR: This book is a core reference for graduate students and CAD professionals and presents a balance of theory and practice in a intuitive manner.
References
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Journal ArticleDOI
The Quadratic Assignment Problem
TL;DR: In this article, the equivalence of the Koopmans-beckmann problem to a linear assignment problem with certain additional constraints is demonstrated, and a method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions.
Journal ArticleDOI
A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities
Gordon C. Armour,Elwood S. Buffa +1 more
TL;DR: A computer program governed by an algorithm which determines how relative location patterns should be altered to obtain sequentially the most improved pattern with each change, commands their alteration, evaluates the results of alterations, and identifies the sub-optimumrelative location patterns.
Journal ArticleDOI
Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem
TL;DR: A recent article by Steinberg as discussed by the authors describes a suboptimal procedure for solving the backboard wiring problem, which is a generalization of the quadratic assignment problem in the more general form in which it was discussed by Koopmans and Beckmann [2].
Journal ArticleDOI
Quadratic Assignment Problem Algorithms and the Location of Indivisible Facilities
TL;DR: In this article, the authors discuss the problem of assigning locations to indivisible facilities and its relation to the quadratic assignment problem and develop two suboptimal algorithms, one dealing with the general assignment problem, and the other with an interesting special case.