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Constant queue routing on a mesh

Sanguthevar Rajasekaran, Richard Overholt
1992 Journal of Parallel and Distributed Computing  
We present a 2n2 step routing algorithm for an n × n mesh that requires a queue size of only 58.  ...  The previous best known result is a routing algorithm with the same time bound but with a queue size of 672. The time bound of 2n2 is optimal.  ...  Other packets will also reach their destination within 2m further steps, even if the (non special) packets present in supersquares < 2, 4 >, < 2, 5 >, < 7, 4 >, and < 7, 5 > at time step 14m − 2 are not  ... 
doi:10.1016/0743-7315(92)90108-y fatcat:q7mr5pf5mbeg3jptqq72fyiwk4

An optimal randomized routing algorithm for the Mesh and a class of efficient Mesh-like routing networks [chapter]

Sanguthevar Rajasekaran, Thanasis Tsantilas
1987 Lecture Notes in Computer Science  
And finally we present a (possibly) non optimal oblivious routing algorithm for the Mesh that requires only O(1) queue size for any node at any time.  ...  In particular we present a randomized oblivious constant queue size routing algorithm that runs in time O(n 1+ ), for any > 0.  ...  Acknowledgement The authors would like to thank John Reif and Leslie Valiant for their constant encouragement and support.  ... 
doi:10.1007/3-540-18625-5_53 fatcat:kefxioerivh4hbvasonchayruq

Mesh connected computers with fixed and reconfigurable buses: packet routing and sorting

S. Rajasekaran
1996 IEEE transactions on computers  
We provide an improved algorithm for 1 − 1 routing and a matching sorting algorithm.  ...  In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k − k routing and k − k sorting on a 2D  ...  Acknowledgements I am thankful to Sunil Shende for introducing me to this area. I also would like to thank Viktor K. Prasanna and Assaf Schuster for providing me with a number of relevant articles.  ... 
doi:10.1109/12.509905 fatcat:ys5nysamy5a2haxawmfquk7geu

Optimal algorithms for the many-to-one routing problem on two-dimensional meshes

Fillia Makedon, Antonios Symvonis
1993 Microprocessors and microsystems  
We give an algorithm that solves the problem in asymptotically optimal time. Furthermore, our algorithm uses queues of small constant size.  ...  We show that there is an instance of the many-to-one packet routing problem that requires n~-k/2 routing steps to be solved, where k is the maximum number of packets a processor can receive.  ...  The nXn mesh is illustrated in Figure 1 . At any one step, each processor can communicate with all of its neighbours by the use of bidirectional links (channels).  ... 
doi:10.1016/0141-9331(93)90056-d fatcat:6g6isbaqrfavjngmybuvnahxrm

Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound [chapter]

Manfred Kunde
1993 Lecture Notes in Computer Science  
This proves that all packets reach their destination row in time under distribution 1 . A similar argument can be given for distribution 2 . 2  ...  It can be shown that all remaining row elements can be routed in this way, and that they reach their destination row in time.  ...  Acknowledgements: I would like to thank Christos Kaklamanis, Greg Plaxton, and Rajmohan Rajaraman for helpful discussions.  ... 
doi:10.1007/3-540-57273-2_62 fatcat:i6er5xsf6vc4fhtynlc6eeuomi

PERMUTATION ROUTING AND SORTING ON THE RECONFIGURABLE MESH

SANGUTHEVAR RAJASEKARAN, THEODORE MCKENDALL
1998 International Journal of Foundations of Computer Science  
A trivial lower bound for routing on M r will be n 2 . On the PARBUS linear array, n is a lower bound and hence any standard n-step routing algorithm will be optimal.  ...  In contrast, 2n2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n2 steps on a conventional mesh.  ...  Our linear array routing algorithm on M r indeed uses reconfiguration in a non trivial manner.  ... 
doi:10.1142/s0129054198000143 fatcat:y3wwhwr4kbhorbuhzkobm236ty

Randomized Algorithms on the Mesh [chapter]

Lata Narayanan
1999 Combinatorial Optimization  
The mesh-connected array is an attractive architecture for parallel machines, and a number of existing parallel machines are based on a mesh topology.  ...  In this paper, we survey the results on three fundamental problems in parallel computation: routing, sorting, and selection, and demonstrate that randomized algorithms for these problems on the mesh are  ...  steps on a nn synchronous SIMD mesh; their algorithm may be adapted to run in 3n+on time on a MIMD mesh.  ... 
doi:10.1007/978-1-4613-3282-4_4 fatcat:nrvuh22a5neldjgysyftydy3ne

Randomized algorithms on the mesh [chapter]

Lata Narayanan
1998 Lecture Notes in Computer Science  
The mesh-connected array is an attractive architecture for parallel machines, and a number of existing parallel machines are based on a mesh topology.  ...  In this paper, we survey the results on three fundamental problems in parallel computation: routing, sorting, and selection, and demonstrate that randomized algorithms for these problems on the mesh are  ...  steps on a nn synchronous SIMD mesh; their algorithm may be adapted to run in 3n+on time on a MIMD mesh.  ... 
doi:10.1007/3-540-64359-1_715 fatcat:5l453vvbzjhrpoyytuwn45dcbu

Dynamic packet routing on arrays with bounded buffers [chapter]

Andrei Z. Broder, Alan M. Frieze, Eli Upfal
1998 Lecture Notes in Computer Science  
We give the first routing algorithm on this topology that is stable under an injection rate within a constant factor of the hardware bandwidth.  ...  We study the performance of packet routing on arrays (or meshes) with bounded buffers in the routing switches, assuming that new packets are continuously inserted at all the nodes.  ...  There is a packet routing algorithm for the nxn mesh with bounded buffers that is stable for any inter-arrival distribution with expectation at least Cn for some fixed constant C.  ... 
doi:10.1007/bfb0054328 fatcat:5gwelvvvl5e5hbq57ctllfscve

Matching the bisection bound for routing and sorting on the mesh

Michael Kaufmann, Sanguthevar Rajasekaran, Jop F. Sibeyn
1992 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92  
We give two different algorithms for k-k routing that run in kn 2 + o(kn) and k 2 n + o(kn) routing steps respectively.  ...  In this paper we present randomized algorithms for kk routing, k-k sorting, and cut through routing on the mesh connected processor array.  ...  Non-stray packets use the same algorithm, i.e., they are sorted.  ... 
doi:10.1145/140901.140905 dblp:conf/spaa/KaufmannRS92 fatcat:5f2eigwtajhg3iurqqvh5m3od4

k-k Routing, k-k Sorting, and Cut-Through Routing on the Mesh

S. Rajasekaran
1995 Journal of Algorithms  
The algorithm for k-k routing runs in [k/2]n+o(kn) steps.  ...  We also show that kk sorting can be accomplished within [$In + n + o(kn) steps, and cut thorugh routing can be done in $kn + f n + o(kn) steps. [10]'s algorithm for kk sorting has a time bound of kn +  ...  Non-stray packets use the same algorithm, i.e., they are sorted.  ... 
doi:10.1006/jagm.1995.1042 fatcat:khrgnkf22vcxlij2j4x45vw2dq

Page 1788 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
(English summary) Algorithms—ESA °94 (Utrecht), 183-201, Lecture Notes in Comput. Sci., 855, Springer, Berlin, 1994. Summary: “We introduce the notion of non-exploratory self- stabilizing algorithms.  ...  A non-exploratory algorithm involves a significant reduc- tion in overall communication complexity.  ... 

A general approach to dynamic packet routing with bounded buffers

Andrei Z. Broder, Alan M. Frieze, Eli Upfal
2001 Journal of the ACM  
In all cases we start from a known static algorithm, and mod& it to fit our framework. In particular we give the first dynamic algorithm for routing on a butte$y with bounded buffers.  ...  Both the injection rate for which the algorithm is stable, and the expected time a packet spends in the system are optimal up to constant factors.  ...  Let z be the non-trivial (that is, n: # 1) root of the equation (the Laplace transform) The expected wait in the queue is then z / ( p ( 1 -z)).  ... 
doi:10.1145/375827.375849 fatcat:ynzwebtf5fd6pojuwzjpqv6nu4

Improved Space Efficient Algorithms for BFS, DFS and Applications [chapter]

Niranka Banerjee, Sankardeep Chakraborty, Venkatesh Raman
2016 Lecture Notes in Computer Science  
We demonstrate the use of our data structure by developing another data structure using it that can represent a sequence of n non-negative integers x1, x2, . . . xn using at most n i=1 xi + 2n + o( n i  ...  We also discuss an algorithm for finding a minimum weight spanning tree of a weighted undirected graph using at most n + o(n) bits. For DFS, we have two kinds of results.  ...  Acknowledgement The authors thank Saket Saurabh for suggesting the exploration of algorithms using O(m + n) bits for DFS and Anish Mukherjee for helpful discussions.  ... 
doi:10.1007/978-3-319-42634-1_10 fatcat:zrj6i756gbgcnmwo76lkxrxy64

Integer sorting on a mesh-connected array of processors

Danny Krizanc
1993 Information Processing Letters  
Using a less restrictive, more realistic model we show that the sorting N = n 2 integers in the range [1 ... N] can be performed in 2n + o(n) steps on a n X n mesh.  ...  Schnorr and Shamir and independently Kunde, have shown that sorting N = n 2 inputs into snake-like ordering on a n X n mesh requires 3n -o(n) steps.  ...  The (non-commutative) operation is defined by(Xl, yd Efl (X2, Y2) = (x}, b) where b = Y2 if X2 = 1 and b = Xl otherwise.Each of the computations done inside the blocks require O( m) steps.  ... 
doi:10.1016/0020-0190(93)90073-i fatcat:cf6rbvna7begpekx3wujtnonai
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