Fault-Tolerant Routing in DeBruijn Comrnunication Networks
IEEE Transactions on Computers
The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI
IEEE Transactions on Computers
Introduction to algorithms
Tight bounds for oblivious routing in the hypercube
SPAA '90 Proceedings of the second 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
A VLSI decomposition of the deBruijn graph
Journal of the ACM (JACM)
Rearrangeable circuit-switched hypercube architectures for routing permutations
Journal of Parallel and Distributed Computing
Deterministic sorting in nearly logarithmic time on the hypercube and related computers
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Packet routing and PRAM emulation on star graphs and leveled networks
Journal of Parallel and Distributed Computing
Routing and Transmitting Problems in de Bruijn Networks
IEEE Transactions on Computers
Selection, routing, and sorting on the star graph
Journal of Parallel and Distributed Computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Parallel Sorting Algorithms
Adaptive and Oblivious Algorithms for D-Cube Permutation Routing
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Routing, merging and sorting on parallel models of computation
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Randomized parallel communication (Preliminary Version)
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Hi-index | 0.00 |
We consider the problems of routing and sorting on a de Bruijn network. First, we show that any deterministic oblivious routing scheme for permutation routing on a d-ary de Bruijn network with N = dn nodes, in the worst case, will take $\Omega (\sqrt N)$ steps under the single-port model. This improves the existing lower bounds provided d is not a constant. We also show that the lower bound is indeed a tight one. Second, we present a deterministic nonoblivious permutation routing algorithm which runs in O(d·n2) time on a d-ary de Bruijn network with N = dn nodes. This algorithm is currently the fastest known nonoblivious deterministic routing algorithm for de Bruijn networks of arbitrary degree. Finally, we present an efficient general sorting algorithm for the de Bruijn networks of arbitrary degree. This algorithm is the best sorting algorithm known so far. It runs in O((log d) ·d·n2) time for directed de Bruijn network with dn nodes, degree d, and diameter n. As a corollary, we show that on a binary de Bruijn network of N nodes, our sorting scheme requires at most 2 log2N steps.