Combinatorica
Better expanders and superconcentrators
Journal of Algorithms
Dynamic load balancing for distributed memory multiprocessors
Journal of Parallel and Distributed Computing
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Isoperimetric numbers of graphs
Journal of Combinatorial Theory Series B
SIAM Journal on Computing
A guided tour of Chernoff bounds
Information Processing Letters
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Load balancing and Poisson equation in a graph
Concurrency: Practice and Experience
Eigenvalues and expansion of regular graphs
Journal of the ACM (JACM)
A Chernoff Bound for Random Walks on Expander Graphs
SIAM Journal on Computing
Efficient schemes for nearest neighbor load balancing
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Tight Analyses of Two Local Load Balancing Algorithms
SIAM Journal on Computing
An asynchronous and iterative load balancing algorithm for discrete load model
Journal of Parallel and Distributed Computing
Local Divergence of Markov Chains and the Analysis of Iterative Load-Balancing Schemes
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On the communication complexity of randomized broadcasting in random-like graphs
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
A new analytical method for parallel, diffusion-type load balancing
Journal of Parallel and Distributed Computing
Distributed Coordination Strategies for Wide-Area Patrol
Journal of Intelligent and Robotic Systems
Discrete load balancing is (almost) as easy as continuous load balancing
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
A new analytical method for parallel, diffusion-type load balancing
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Dynamic diffusion load balancing
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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Diffusive schemes have been widely analyzed for parallel and distributed load balancing. It is well known that their convergence rates depend on the eigenvalues of some associated matrices and on the expansion properties of the underlying graphs. In the first part of this paper we make use of these relationships in order to obtain new spectral bounds on the edge and node expansion of graphs. We show that these new bounds are better than the classical bounds for several graph classes. In the second part of the paper, we consider the load balancing problem for indivisible unit size tokens. Since known diffusion schemes do not completely balance the load for such settings, we propose a randomized distributed algorithm based on Markov chains to reduce the load imbalance. We prove that this approach provides the best asymptotic result that can be achieved in l1- or l2-norm concerning the final load situation.