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K.W. Ryu, J. JáJ?, "Efficient Algorithms for List Ranking and for Solving Graph Problems on the Hypercube," IEEE Transactions on Parallel and Distributed Systems, vol. 1, no. 1, pp. 8390, January, 1990.  
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@article{ 10.1109/71.80127, author = {K.W. Ryu and J. JáJ?}, title = {Efficient Algorithms for List Ranking and for Solving Graph Problems on the Hypercube}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {1}, number = {1}, issn = {10459219}, year = {1990}, pages = {8390}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.80127}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Efficient Algorithms for List Ranking and for Solving Graph Problems on the Hypercube IS  1 SN  10459219 SP83 EP90 EPD  8390 A1  K.W. Ryu, A1  J. JáJ?, PY  1990 KW  Index Termsload balancing; graph algorithms; sorting; list ranking; graph problems; hypercube algorithm; linear speedup; hypercube algorithms; basic graph problems; tree expression evaluation; biconnected components; ear decomposition; stnumbering; oneport communication; computational complexity; graph theory; parallel algorithms; sorting VL  1 JA  IEEE Transactions on Parallel and Distributed Systems ER   
A hypercube algorithm to solve the list ranking problem is presented. Let n be the length of the list, and let p be the number of processors of the hypercube. The algorithm described runs in time O(n/p) when n= Omega (p/sup 1+ epsilon /) for any constant epsilon, and in time O(n log n/p+log/sup 3/ p) otherwise. This clearly attains a linear speedup when n= Omega (p/sup 1+ epsilon /). Efficient balancing and routing schemes had to be used to achieve the linear speedup. The authors use these techniques to obtain efficient hypercube algorithms for many basic graph problems such as tree expression evaluation, connected and biconnected components, ear decomposition, and stnumbering. These problems are also addressed in the restricted model of oneport communication.
[1] A. Aggarwal and M. A. Huang, "Network complexity of sorting and graph problems and simulating CRCW PRAMS by interconnection networks," inProc. 3rd Aegean Workshop Comput., AWOC 88, Corfu, Greece, June/July 1988, pp. 339350.
[2] M. Atallah and U. Vishkin, "Finding Euler tours in parallel,"J. Syst. Sci., vol. 29, pp. 330337, 1984.
[3] F. Y. Chin, J. Lam, and INgo Chen, "Efficient parallel algorithms for some graph problems,"CACM, vol. 25, pp. 659665, 1982.
[4] R. Cole and U. Vishkin, "Deterministic coin tossing and accelerating cascades: Micro and macro techniques for designing parallel algorithms," inProc. 18th ACM Symp. Theory Comput., 1986, pp. 206219.
[5] R. Cole and U. Vishkin, "Approximate parallel scheduling. Part 2: Applications to logarithmictime optimal parallel graph algorithms," to be published.
[6] D. Eppstein and Z. Galil, "Parallel algorithmic techniques for combinatorial computation," Feb. 1988.
[7] Y. Y. Zhang and P. S. P. Wang, "A modified parallel thinning algorithm," inProc. 9th Int. Conf. Patt. Recogn.(Rome, Italy), 1988, pp. 10231025.
[8] T. Hagerup, "Towards optimal parallel bucket sorting,"Inform. Computation, vol. 75, pp. 3951, 1987.
[9] T. Hagerup, "Optimal parallel algorithms on planar graphs," inProc. 3rd Aegean Workshop on Computing, AWOC 88, Corfu, Greece, June/ July 1988, pp. 2432.
[10] Y. Han, "Designing fast and efficient parallel algorithms," Ph.D. dissertation. Dep. Computer Sci., Duke Univ., 1987.
[11] Y. Han, "An optimal parallel algorithm for computing linked list prefix," TR No. 10087, Dep. Comput. Sci., Univ. Kentucky, Lexington, 1987.
[12] C. T. Ho and S. L. Johnson, "Algorithms for matrix transposition on Booleanncube configured ensemble architectures," inProc. 1987 International Conf. Parallel Process., 1987, pp. 621629.
[13] J. JáJáand K. W. Ryu, "Load balancing and routing on the hypercube and related networks," UMIACSTR8961, CSTR2264, Univ. Maryland, June 1989.
[14] S. L. Johnsson, "Communication efficient basic linear algebra computations on hypercube architectures,"J. Parallel Distributed Comput., pp. 133172, 1987.
[15] R. M. Karp and V. Ramachandran, "A survey of parallel algorithms for sharedmemory machines," Tech. Rep., Comput. Sci. Division, Univ. of California, Berkeley, CA, 1988.
[16] S. R. Kosaraju and A. L. Delcher, "Optimal parallel evaluation of treestructured computations by raking, " inProc. 3rd Aegean Workshop on Computing, AWOC 88, Corfu, Greece, June/July 1988, pp. 101 110.
[17] F.T. Leighton, "Tight bounds on the complexity of parallel sorting," inProc. 16th Annu. ACM Symp. Theory Computing, Washington, DC, May 1984, pp. 7180.
[18] Y. Maon, B. Schieber and U. Vishkin, "Parallel ear decomposition search (EDS) andstnumbering in graphs,"Theoretical Comp. Sci., vol. 47, pp. 277298, 1986.
[19] Y. Saad and M. H. Schultz, "Topological properties of hypercubes," TR YALEU/DCS/RR389, Yale Univ. New Haven, CT, June 1985.
[20] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 2233, Jan. 1985.
[21] B. Schieber and U. Vishkin, "On finding lowest common ancestors: Simplification and parallelization,"SIAM J. Comput, vol. 17, no. 6, pp. 12531262. Dec. 1988.
[22] Y. Shiloach and U. Vishkin, "An O(log n) parallel connectivity algorithm,"J. Algorithms, vol. 3, pp. 5767, 1982.
[23] R. E. Tarjan and U. Vishkin, "An efficient parallel biconnectivity algorithm,"SIAM J. Comput., vol. 14, no. 4, pp. 862874, Nov. 1985.
[24] P. Varman and K. Doshi, "Sorting with linear speedup in a VLSI network," inProc. 1988 Internat. Conf. Parallel Processing, 1988, pp. 202206.
[25] U. Vishkin, "An optimal parallel connectivity algorithm,"Disc App. Math., vol. 9, pp. 197207, 1984.
[26] U. Vishkin, "On efficient parallel strong orientation,"Infor. Proc. Lett., vol. 20, pp. 235240, June 1985.
[27] J. C. Wyllie, "The complexity of parallel computation," TR 79387, Dep. Comput. Sci., Cornell Univ., Ithaca, NY, 1979.