A Subspace Semidefinite Programming for Spectral Graph Partitioning
نویسندگان
چکیده
A semidefinite program (SDP) is an optimization problem over n × n symmetric matrices where a linear function of the entries is to be minimized subject to linear equality constraints, and the condition that the unknown matrix is positive semidefinite. Standard techniques for solving SDP’s require O(n) operations per iteration. We introduce subspace algorithms that greatly reduce the cost os solving large-scale SDP’s. We apply these algorithms to SDP approximations of graph partitioning problems. We numerically compare our new algorithm with a standard semidefinite programming algorithm and show that our subspace algorithm performs better.
منابع مشابه
Semidefinite Programmingfor Graph Partitioning with Preferencesin Data Distribution
Graph partitioning with preferences is one of the data distribution models for parallel computer, where partitioning and mapping are generated together. It improves the overall throughput of message traffic by having communication restricted to processors which are near each other, whenever possible. This model is obtained by associating to each vertex a value which reflects its net preference ...
متن کاملSemidefinite spectral clustering
Multi-way partitioning of an undirected weighted graph where pairwise similarities are assigned as edge weights, provides an important tool for data clustering, but is an NP-hard problem. Spectral relaxation is a popular way of relaxation, leading to spectral clustering where the clustering is performed by the eigen-decomposition of the (normalized) graph Laplacian. On the other hand, semidefin...
متن کاملA note on Fiedler vectors interpreted as graph realizations
The second smallest eigenvalue of the Laplace matrix of a graph and its eigenvectors, also known as Fiedler vectors in spectral graph partitioning, carry significant structural information regarding the connectivity of the graph. Using semidefinite programming duality we offer a geometric interpretation of this eigenspace as optimal solution to a graph realization problem. A corresponding inter...
متن کاملFast Approximation Algorithms for Graph Partitioning Using Spectral and Semidefinite-Programming Techniques
Fast Approximation Algorithms for Graph Partitioning Using Spectral and Semidefinite-Programming Techniques by Lorenzo Orecchia Doctor of Philosophy in Computer Science University of California, Berkeley Professor Satish Rao, Chair Graph-partitioning problems are a central topic of research in the study of approximation algorithms. They are of interest to both theoreticians, for their far-reach...
متن کاملA Copositive Programming Approach to Graph Partitioning
We consider 3-partitioning the vertices of a graph into sets S1, S2 and S3 of specified cardinalities, such that the total weight of all edges joining S1 and S2 is minimized. This problem is closely related to several NP-hard problems like determining the bandwidth or finding a vertex separator in a graph. We show that this problem can be formulated as a linear program over the cone of complete...
متن کامل