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## Filters

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Constant queue routing on a mesh

1992
*
Journal of Parallel and Distributed Computing
*

We present

doi:10.1016/0743-7315(92)90108-y
fatcat:q7mr5pf5mbeg3jptqq72fyiwk4
*a**2n*−*2**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*2n*−*2*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 ...##
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An optimal randomized routing algorithm for the Mesh and a class of efficient Mesh-like routing networks
[chapter]

1987
*
Lecture Notes in Computer Science
*

And finally we present

doi:10.1007/3-540-18625-5_53
fatcat:kefxioerivh4hbvasonchayruq
*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. ...##
###
Mesh connected computers with fixed and reconfigurable buses: packet routing and sorting

1996
*
IEEE transactions on computers
*

We provide

doi:10.1109/12.509905
fatcat:ys5nysamy5a2haxawmfquk7geu
*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. ...##
###
Optimal algorithms for the many-to-one routing problem on two-dimensional meshes

1993
*
Microprocessors and microsystems
*

We give

doi:10.1016/0141-9331(93)90056-d
fatcat:6g6isbaqrfavjngmybuvnahxrm
*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). ...##
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Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound
[chapter]

1993
*
Lecture Notes in Computer Science
*

This proves that all packets reach their destination row

doi:10.1007/3-540-57273-2_62
fatcat:i6er5xsf6vc4fhtynlc6eeuomi
*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. ...##
###
PERMUTATION ROUTING AND SORTING ON THE RECONFIGURABLE MESH

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,

*2n*−

*2*is the diameter of

*a*conventional mesh and hence

*routing*and sorting will need at least

*2n*−

*2*

*steps*on

*a*conventional mesh. ... Our linear

*array*

*routing*

*algorithm*on M r indeed uses reconfiguration

*in*

*a*

*non*trivial manner. ...

##
###
Randomized Algorithms on the Mesh
[chapter]

1999
*
Combinatorial Optimization
*

The mesh-connected

doi:10.1007/978-1-4613-3282-4_4
fatcat:nrvuh22a5neldjgysyftydy3ne
*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. ...##
###
Randomized algorithms on the mesh
[chapter]

1998
*
Lecture Notes in Computer Science
*

The mesh-connected

doi:10.1007/3-540-64359-1_715
fatcat:5l453vvbzjhrpoyytuwn45dcbu
*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. ...##
###
Dynamic packet routing on arrays with bounded buffers
[chapter]

1998
*
Lecture Notes in Computer Science
*

We give the first

doi:10.1007/bfb0054328
fatcat:5gwelvvvl5e5hbq57ctllfscve
*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. ...##
###
Matching the bisection bound for routing and sorting on the mesh

1992
*
Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92
*

We give two different

doi:10.1145/140901.140905
dblp:conf/spaa/KaufmannRS92
fatcat:5f2eigwtajhg3iurqqvh5m3od4
*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. ...##
###
k-k Routing, k-k Sorting, and Cut-Through Routing on the Mesh

1995
*
Journal of Algorithms
*

The

doi:10.1006/jagm.1995.1042
fatcat:khrgnkf22vcxlij2j4x45vw2dq
*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. ...##
###
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

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)). ...

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

2016
*
Lecture Notes in Computer Science
*

We demonstrate the use of our data structure by developing another data structure using it that can represent

doi:10.1007/978-3-319-42634-1_10
fatcat:zrj6i756gbgcnmwo76lkxrxy64
*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. ...##
###
Integer sorting on a mesh-connected array of processors

1993
*
Information Processing Letters
*

Using

doi:10.1016/0020-0190(93)90073-i
fatcat:cf6rbvna7begpekx3wujtnonai
*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*. ...
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