Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Optimal speedup for backtrack search on a butterfly network
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Coding theory, hypercube embeddings, and fault tolerance
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Tight bounds for on-line tree embeddings
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Branch-and-bound and backtrack search on mesh-connected arrays of processors
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Dynamic tree embeddings in butterflies and hypercubes
SIAM Journal on Computing
Taking random walks to grow trees in hypercubes
Journal of the ACM (JACM)
Randomized parallel algorithms for backtrack search and branch-and-bound computation
Journal of the ACM (JACM)
Randomized algorithms
Performance analysis for dynamic tree embedding in k-partite networks by a random walk
Journal of Parallel and Distributed Computing - Special issue on irregular problems in supercomputing applications
Lower bounds for dynamic tree embedding in bipartite networks
Journal of Parallel and Distributed Computing
Randomized load distribution of arbitrary trees in distributed networks
SAC '98 Proceedings of the 1998 ACM symposium on Applied Computing
Efficient Dynamic Embedding of Arbitrary Binary Trees into Hypercubes
IRREGULAR '96 Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems
A proof of alon's second eigenvalue conjecture
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the performance of randomized embedding of reproduction trees in static networks
International Journal of Parallel Programming
Analysis of randomized load distribution for reproduction trees in linear arrays and rings
Theoretical Computer Science
Rapidly Mixing Random Walks on Hypercubes with Application to Dynamic Tree Evolution
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Concurrency and Computation: Practice & Experience - Systems Performance Evaluation
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
FCST '09 Proceedings of the 2009 Fourth International Conference on Frontier of Computer Science and Technology
| Hi-index | 0.00 |
Tree-structured computations are among the most popular and important and powerful computing paradigms in computer science. In many such applications, the size and shape of a tree that represents a parallel computation is dynamic and unpredictable at compile time. The tree evolves gradually during the course of the computation. When such an application is executed on a multicomputer system with a static network, the dynamic tree evolution problem is to distribute the tree nodes to the processors of the network such that all the processors receive roughly the same amount of load and that communicating nodes are assigned to neighboring processors. The main contribution of the paper is to conduct a unified study of dynamic tree evolution on regular networks. Our regular networks include d-dimensional torus networks, d-dimensional lattice networks, complete d-partite networks, and random regular networks. These networks include several fundamental networks such as rings, k-ary d-cubes, complete networks, and hypercubes as special cases. We describe a simple random-walk-based asymptotically optimal dynamic tree evolution algorithm on regular networks and analyze the exponential speed at which the performance ratio converges to the optimal. Our strategy is to prove that the Markov chain of a random walk on a regular network is rapidly mixing in the sense that, starting from any initial distribution, the Markov chain converges to its stationary distribution in a small number of steps. We also show that larger dilation results in better tree node distribution.