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Combinatorica - Theory of Computing
The random walk construction of uniform spanning trees and uniform labelled trees
SIAM Journal on Discrete Mathematics
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Randomized algorithms
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Balls and bins: a study in negative dependence
Random Structures & Algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Compact name-independent routing with minimum stretch
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A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
On certain connectivity properties of the internet topology
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Finding Disjoint Paths in Expanders Deterministically and Online
FOCS '07 Proceedings of the 48th 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
Generating random spanning trees
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Proceedings of the ACM SIGCOMM 2008 conference on Data communication
Proceedings of the forty-first annual ACM symposium on Theory of computing
Proceedings of the 28th ACM symposium on Principles of distributed computing
Electric Routing and Concurrent Flow Cutting
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Expansion and the cover time of parallel random walks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
A general framework for graph sparsification
Proceedings of the forty-third annual ACM symposium on Theory of computing
Electric routing and concurrent flow cutting
Theoretical Computer Science
Physical expander in virtual tree overlay
DISC'11 Proceedings of the 25th international conference on Distributed computing
Journal of the ACM (JACM)
Spectral sparsification of graphs: theory and algorithms
Communications of the ACM
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Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees approximates the expansion of every cut of the graph to within a factor of O(log n). For the random graph Gn, p, for p = Ω(log n/n), we give a randomized algorithm for constructing two spanning trees whose union is an expander. This is suggested by the case of the complete graph, where we prove that two random spanning trees give an expander. The construction of the splicer is elementary; each spanning tree can be produced independently using an algorithm by Aldous and Broder: A random walk in the graph with edges leading to previously unvisited vertices included in the tree. Splicers also turn out to have applications to graph cut-sparsification where the goal is to approximate every cut using only a small subgraph of the original graph. For random graphs, splicers provide simple algorithms for sparsifiers of size O(n) that approximate every cut to within a factor of O(log n).