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Sanguthevar Rajasekaran, "Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing and Sorting," IEEE Transactions on Computers, vol. 45, no. 5, pp. 529539, May, 1996.  
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@article{ 10.1109/12.509905, author = {Sanguthevar Rajasekaran}, title = {Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing and Sorting}, journal ={IEEE Transactions on Computers}, volume = {45}, number = {5}, issn = {00189340}, year = {1996}, pages = {529539}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.509905}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing and Sorting IS  5 SN  00189340 SP529 EP539 EPD  529539 A1  Sanguthevar Rajasekaran, PY  1996 KW  Reconfigurable networks KW  mesh KW  mesh with reconfigurable buses KW  mesh with fixed buses KW  sorting KW  packet routing KW  k−k routing KW  k−k sorting KW  randomized algorithms KW  parallel computing. VL  45 JA  IEEE Transactions on Computers ER   
Abstract—Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing and sorting on these models. 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)
[1] D. Angluin and L.G. Valiant,"Fast Probabilistic Algorithms for Hamiltonian Paths and Matchings," J. Computer and Systems Science, vol. 18, pp. 155193, 1979.
[2] Y. BenAsher,D. Peleg,R. Ramaswami,, and A. Schuster,“The power of reconfiguration,” J. of Parallel and Distributed Computing, vol. 13, no. 2, pp. 139153, Oct. 1991.
[3] H. Chernoff,"A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations," Annals of Mathematical Statistics, vol. 23, pp. 493507, 1952.
[4] J.C. Cogolludo and S. Rajasekaran,"Permutation Routing on Reconfigurable Meshes," Proc. Int'l Symp. Algorithms and Computation, Lecture Notes in Computer Science 762, pp. 157166, SpringerVerlag, 1993.
[5] J. Jang and V.K. Prasanna,“An optimal sorting algorithm on reconfigurable mesh,” Proc. Int’l Parallel Processing Symp., pp. 130137, Mar. 1992.
[6] J. Jenq and S. Sahni,“Histogramming on a reconfigurable mesh computer,” Proc. Int’l Parallel Processing Symp., pp. 425432, 1992.
[7] C. Kaklamanis and D. Krizanc,"Optimal Sorting on Mesh Connected Processor Arrays," Proc. ACM Symp. Parallel Algorithms and Architectures, pp. 5059, 1992.
[8] M. Kaufmann,S. Rajasekaran, and J. Sibeyn,"Matching the Bisection Bound for Routing and Sorting on the Mesh," Proc. ACM Symp. Parallel Algorithms and Architectures, pp. 3140, 1992.
[9] D. Krizanc,S. Rajasekaran, and S. Shende,"A Comparison of Meshes with Static Buses and Unidirectional WrapArounds," Parallel Processing Letters, vol. 3, no. 2, pp. 109114, June 1993.
[10] V.K. Prasanna Kumar, and C.S. Raghavendra,“Array processor with multiple broadcasting,” J. of Parallel and Distributed Computing, vol. 4, pp. 173190, 1987.
[11] M. Kunde,"Concentrated Regular Data Streams on Grids: Sorting and Routing Near to the Bisection Bound," Proc. IEEE Symp. Foundations of Computer Science, pp. 141150, 1991.
[12] F.T. Leighton,"Average Case Analysis of Greedy Routing Algorithms on Arrays," Proc. Second Ann. ACM Symp. Parallel Algorithms and Architectures, SPAA '90, Crete, July26, 1990.
[13] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[14] F.T. Leighton,F. Makedon, and I.G. Tollis,"A 2n  2 Algorithm for Routing in an n×n Array With Constant Size Queues," Proc. ACM Symp. Parallel Algorithms and Architectures, SPAA'89, pp. 328335, June 1989.
[15] J.YT. Leung and S.M. Shende,"Packet Routing on Square Meshes with Row and Column Buses," Proc. IEEE Symp. Parallel and Distributed Processing, pp. 834837, Dec. 1991.
[16] R. Miller,V.K. Prasanna Kumar,D.I. Reisis,, and Q.F. Stout,“Meshes with reconfigurable buses,” MIT Conf. on Advanced Research in VLSI, pp. 163178, 1988.
[17] M. Nigam and S. Sahni, "Sorting n Numbers on n x n Reconfigurable Meshes With Buses," Proc. Int'l Parallel Processing Symp., pp. 174181, 1993.
[18] S. Olariu,J.L. Schwing, and J. Zhang,"Fundamental Algorithms on Reconfigurable Meshes," Proc. 29th Allerton Conf. Comm., Control, and Computing, pp. 811820, 1991.
[19] C. Raghavendra and V. Kumar,“Permutations on ILLIAC IVtype networks,”IEEE Trans. Comput., pp. 662–669, 1986.
[20] S. Rajasekaran,"Sorting and Selection on Interconnection Networks," DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 21, pp. 275296, 1995.
[21] S. Rajasekharan, "Randomized Parallel Selection," Proc. Symp. Foundations of Software Technology and Theoretical Computer Science, pp. 215224, 1990.
[22] S. Rajasekaran, “$k$$k$Routing,$k$$k$Sorting, and Cutthrough Routing on the Mesh,” J. Algorithms, vol. 19, no. 3, pp. 361–382, 1995.
[23] S. Rajashekaran,“Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing, Sorting and Selection,” Manuscript, Dept. of CIS, Univ. of Pennsylvania, Oct. 1993. Also, appears at the First Ann. European Symp. on Algorithms, 1993.
[24] S. Rajasekaran and T. McKendall,"Permutation Routing and Sorting on the Reconfigurable Mesh," Technical Report MSCIS9236, Dept. of Computer and Information Science, Univ. of Pennsylvania, May 1992.
[25] S. Rajasekaran and R. Overholt,"Constant Queue Routing on a Mesh," Proc. Symp. Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 480, pp. 444455, SpringerVerlag, 1990. Also in J. Parallel and Distributed Computing, vol. 15, pp. 160166, 1992.
[26] S. Rajasekaran and M. Raghavachari,"Optimal Randomized Algorithms for Multipacket and Cut Through Routing on the Mesh," J. Parallel and Distributed Computing, vol. 26, pp. 257260, 1995.
[27] S. Rajasekaran and J.H. Reif,"Derivation of Randomized Sorting and Selection Algorithms," Parallel Algorithm Derivation And Program Transformation, Paige, Reif, and Wachter, eds., pp.187205, Kluwer Academic, 1993.
[28] S. Rajasekaran and Th. Tsantilas,"Optimal Routing Algorithms for MeshConnected Processor Arrays," Algorithmica, 8, pp. 2138, 1992.
[29] J.H. Reif and L.G. Valiant, "A Logarithmic Time Sort for Linear Size Networks," J. ACM, vol. 34, pp. 6076, Jan. 1987.
[30] C. Schnorr and A. Shamir,“An optimal sorting algorithm for mesh connected computers,”inProc. 18th ACM Symp. on Theory of Comput., 1986, pp. 263–271.
[31] A. Schuster,"Dynamic Reconfiguring Networks for Parallel Computers: Algorithms and Complexity Bounds," PhD thesis, Computer Science Dept., TechnionIsrael Inst. of Tech nology, Aug. 1991.
[32] Q.F. Stout,"Meshes with Multiple Buses," Proc. IEEE Symp. Foundations of Computer Science, pp. 264273, 1986.
[33] L.G. Valiant,"Parallelism in Comparison Problems," SIAM J. Computing, vol. 14 pp. 348355, 1985.