Algorithms, graph theory, and the solution of laplacian linear equations

Authors:
Daniel A. Spielman
Affiliations:
Departments of Computer Science and Mathematics, Program in Applied Mathematics, Yale University
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Year:
2012

Citing 15
Cited 1

A Graph-Theoretic Game and its Application to the $k$-Server Problem

SIAM Journal on Computing
Topics in optimization and sparse linear systems

Topics in optimization and sparse linear systems
Support Theory for Preconditioning

SIAM Journal on Matrix Analysis and Applications
Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Support-Graph Preconditioners

SIAM Journal on Matrix Analysis and Applications
Local Graph Partitioning using PageRank Vectors

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Graph sparsification by effective resistances

STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Lower-Stretch Spanning Trees

SIAM Journal on Computing
Nearly Tight Low Stretch Spanning Trees

FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Finding sparse cuts locally using evolving sets

Proceedings of the forty-first annual ACM symposium on Theory of computing
Twice-ramanujan sparsifiers

Proceedings of the forty-first annual ACM symposium on Theory of computing
Approaching Optimality for Solving SDD Linear Systems

FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Nearly-m log n Time Solver for SDD Linear Systems

FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Using petal-decompositions to build a low stretch spanning tree

STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximating the exponential, the lanczos method and an Õ(m)-time spectral algorithm for balanced separator

STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing

A simple, combinatorial algorithm for solving SDD systems in nearly-linear time

Proceedings of the forty-fifth annual ACM symposium on Theory of computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this talk, we survey major developments in the design of algorithms for solving Laplacian linear equations, by which we mean systems of linear equations in the Laplacian matrices of graphs and their submatrices. We begin with a few examples of where such equations arise, including the analysis of networks of resistors, the analysis of networks of springs, and the solution of maximum flow problems by interior point methods.