Summary
This chapter serves as an introduction to the study of parallel algorithms, in particular how they differ from conventional algorithms, how they are designed, and how they are analyzed to evaluate their speed and cost.
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References
Abrahamson, K., Dadoun, N., Kirkpatrick, D., Prztycka, T., A simple parallel tree contraction algorithm, Journal of Algorithms 10, 1989, 187–302.
Aggarwal, A., Optimal bounds for finding maximum on array of processors with k global buses, IEEE Transactions on Computers 35, 1986, 62–64.
Aggarwal, A., Chazelle, B., Guibas, L.J., O’Dúnlaing, C., Yap, C.K., Parallel computational geometry, Algorithmica 3, 1988, 293–327.
Akers, S.B., Harel, D., Krishnamurthy, B., The star graph: An attractive alternative to the n-cube, Proc. of the International Conference on Parallel Processing, 1987, 393–400.
Akers, S.B., Krishnamurthy, B., The fault tolerance of star graphs, Proc. of the International Conference on Supercomputing 3, 1987, 270–276.
Akers, S.B., Krishnamurthy, B., A group theoretic model for symmetric interconnection networks, IEEE Transactions on Computers 38, 1989, 555–566.
Akl, S.G., Parallel Sorting Algorithms, Academic Press, Orlando, Florida, 1985.
Akl, S.G., The Design and Analysis of Parallel Algorithms, Prentice Hall, Englewood Cliffs, New Jersey, 1989.
Aid, S.G., Parallel synergy, Parallel Algorithms and Applications 1, 1993, 3–9.
Akl, S.G., Parallel Computation: Models and Methods, Prentice Hall, Upper Saddle River, New Jersey, 1997.
Akl, S.G., Bruda, S.D., Parallel real-time optimization: Beyond speedup, Technical Report No. 1999–421, Department of Computing and Information Science, Queen’s University, Kingston, Ontario, January 1999.
Akl, S.G., Chen, L., Efficient parallel algorithms on proper circular arc graphs, IEICE Transactions on Information and Systems, Special Issue on Architecture, Algorithms and Networks for Massively Parallel Computing E79-D, 1996, 1015–1020.
Akl, S.G., Duprat, J., Ferreira, A.G., Hamiltonian circuits and paths in star graphs, I. Dimov, O. Toney (eds.), Advances in Parallel Algorithms, IOS Press, Sofia, Bulgaria, 1994, 131–143.
Akl, S.G., Guenther, G.R., Broadcasting with selective reduction, Proc. of the IFIP Congress, 1989, 515–520.
Aid, S.G., Guenther, G.R., Applications of broadcasting with selective reduction to the maximal sum subsegment problem, International Journal of High Speed Computing 3, 1991, 107–119.
Akl, S.G., Fava Lindon, L., Paradigms admitting superunitary behavior in parallel computation, Proc. of the Joint Conference on Vector and Parallel Processing (CONPAR), Lecture Notes in Computer Science, No. 854, Springer-Verlag, Berlin, 1994, 301–312.
Aid, S.G., Fava Lindon, L., Paradigms for superunitary behavior in parallel computations, Parallel Algorithms and Applications 11, 1997, 129–153.
Aid, S.G., Fava Lindon, L., Guenther, G.R., Broadcasting with selective reduction on an optimal PRAM circuit, Technique et Science Informatiques 10, 1991, 261–268.
Aid, S.G., Lyons, K.A., Parallel Computational Geometry, Prentice Hall, Englewood Cliffs, New Jersey, 1993.
Aid, S.G., Qiu, K., Les réseaux d’interconnexion star et pancake, M. Cosnard, M. Nivat, Y. Robert (eds.), Algorithmique parallèle, Masson, Paris, 1992, 171–181.
Akl, S.G., Qiu, K., A novel routing scheme on the star and pancake networks and its applications, Parallel Computing 19, 1993, 95–101.
Akl, S.G., Qiu, K., Stojmenovie, I., Computing the Voronoi diagram on the star and pancake interconnection networks, Proc. of the Canadian Conference on Computational Geometry, 1992, 353–358.
Akl, S.G., Qiu, K., Stojmenovie, I., Fundamental algorithms for the star and pancake interconnection networks with applications to computational geometry, Networks, Special Issue on Interconnection Networks and Algorithms 23, 1993, 215–226.
Aid, S.G., Stojmenovié, I., Multiple criteria BSR: An implementation and applications to computational geometry problems, Proc. of the Hawaii International Conference on System Sciences 2, 1994, 159–168.
Akl, S.G., Stojmenovié, I., Broadcasting with selective reduction: A powerful model of parallel computation, A.Y. Zomaya (ed.), Parallel and Distributed Computing Handbook, McGraw-Hill, New York, 1996, 192–222.
Ald, S.G., Wolff, T., Efficient sorting on the star graph interconnection network, Proc. of the Annual Allerton Conference, 1997.
Alnuweiri, H.M., Constant-time parallel algorithm for image labeling on a reconfigurable network of processors, IEEE Transactions on Parallel and Distributed Systems 5, 1994, 321–326.
Anderson, R., Miller, G., Deterministic parallel list ranking, Algorithmica 6, 1991, 859–868.
Atallah, M.J., Goodrich, M.T., Efficient parallel solutions to some geometric problems, Journal of Parallel and Distributed Computing 3, 1986, 492–507.
Batcher, K.E., Sorting networks and their applications, Proc. of the AFIPS Spring Joint Computer Conference, 1968, 307–314.
C.L. Wu, T.S. Feng (eds.), Interconnection networks for parallel and distributed processing, IEEE Computer Society, 1984, 576–583.
Ben-Asher, Y., Shuster, A, Ranking on reconfigurable networks, Parallel Processing Letters 1, 1991, 149–156.
Bhagavathi, D., Olariu, S., Shen, W., Wilson, L., A unifying look at semigroup computations on meshes with multiple broadcasting, Parallel Processing Letters 4, 1994, 73–82.
Blelloch, G.E., Vector Models for Data-Parallel Computing, MIT Press, Cambridge, Massachusetts, 1990.
Bokhari, S.H., Finding maximum on an array processor with a global bus, IEEE Transactions on Computers 33, 1984, 133–139.
Bruda, S.D., Aid, S.G., On the data-accumulating paradigm, Proc. Of the Fourth International Conference on Computer Science and Informatics, 1998, 150–153.
Bruda, S.D., Aid, S.G., A case study in real-time parallel computation: Correcting algorithms, Technical Report No. 1998–420, Department of Computing and Information Science, Queen’s University, Kingston, Ontario, December 1998.
Bruda, S.D., Aid, S.G., The characterization of data-accumulating algorithms, Proc. of the International Parallel Processing Symposium, 1999.
Chen, C.C.Y., Das, S.K., Aid, S.G., A unified approach to parallel depth-first traversals of general trees, Information Processing Letters 38, 1991, 49–55.
Chen, L., Optimal bucket sorting and overlap representations. Parallel Algorithms and Applications 10, 1997, 249–269.
Chen, Y.C., Chen, W.T., Chen, G.H., Sheu, J.P., Designing efficient parallel algorithms on mesh-connected computers with multiple broadcasting, IEEE Transactions on Parallel and Distributed Systems 1, 1990, 241–245.
Chiang, W.K., Chen, R.J., The (n, k)-star graph: A generalized star graph, Information Processing Letters 56, 1995, 259–264.
Chiarulli, D.M., Melhem, R.G., Levitan, S.P., Using coincident optical pulses for parallel memory addressing, The Computer Journal 30, 1987, 48–57.
Cole, R., Parallel merge sort, SIAM Journal on Computing 17, 1988, 770–785.
Cole, R., Vishkin, U., Approximate and exact parallel scheduling with applications to list, tree, and graph problems, Proc. of the IEEE Symposium on Foundations of Computer Science, 1986, 478–491.
Cole, R., Vishkin, U., Deterministic coin tossing and accelerating cascades: Micro and macro techniques for designing parallel algorithms, Proc. of the ACM Symposium on Theory of Computing, 1986, 206–219.
CV86c] Cole, R., Vishkin, U., Deterministic coin tossing with applications to optimal parallel list ranking, Information and Control 70 1986, 32–53.
Cole, R., Vishkin, U., Approximate parallel scheduling, Part 1: The basic technique with applications to optimal list ranking in logarithmic time, SIAM Journal on Computing 17, 1988, 128–142.
Cole, R., Vishkin, U., Faster optimal parallel prefix sums and list rank- ing, Information and Control 81, 1989, 334–352.
Coppersmith, D., Winograd, S., Matrix multiplication via arithmetic progressions, Proc. of the ACM Symposium on Theory of Computing, 1987, 1–6.
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Introduction to Algorithms, McGraw-Hill, New York, 1990.
Das, S.K., Deo, N., Prasad, S., Parallel graph algorithms for hypercube computers, Parallel Computing 13, 1990, 143–158.
Dekel, E., Nassimi, D., Salmi, S., Parallel matrix and graph algorithms, SIAM Journal on Computing 10, 1981, 657–675.
Dietzfelbinger, M., Madhavapeddy, S., Sudborough, I.H., Three disjoint path paradigms in star networks, Proc. of the IEEE Symposium on Parallel and Distributed Processing, 1991, 400–406.
Dowd, M., Perl, Y., Rudolph, L., Saks, M., The balanced sorting network, Proc. of the Conference on Principles of Distributed Computing, 1983, 161–172.
Eppstein, D., Galil, Z., Parallel algorithmic techniques for combinatorial computation, Annual Review of Computer Science 3, 1988, 233–283.
Fava Lindon, L., Discriminating analysis and its application to matrix by vector multiplication on the CRCW PRAM, Parallel Processing Letters 2, 1992, 43–50.
Fava Lindon, L., Synergy in Parallel Computation, Ph.D. Thesis, Department of Computing and Information Science, Queen’s University, Kingston, Ontario, 1996.
Fava Lindon, L., Akl, S.G., An optimal implementation of broadcasting with selective reduction, IEEE Transactions on Parallel and Distributed Systems 4, 1993, 256–269.
Ferreira, A.G., Parallel and communication algorithms on hypercube multiprocessors, A.Y. Zomaya (ed.), Parallel and Distributed Computing Handbook, McGraw-Hill, New York, 1996, 568–589.
Fox, G.C., Johnson, M.A., Lyzenga, G.A., Otto, S.W., Salmon, J.K., Walker, D.W., Solving Problems on Concurrent Processors 1, Prentice Hall, Englewood Cliffs, New Jersey, 1988.
Fragopoulou, P., Communication and Fault Tolerance Algorithms on a Class of Interconnection Networks, Ph.D. Thesis, Department of Computing and Information Science, Queen’s University, Kingston, Ontario, 1995.
Fragopoulou, P., Akl, S.G., A parallel algorithm for computing Fourier transforms on the star graph, IEEE Transactions on Parallel and Distributed Systems 5, 1994, 525–531.
Fragopoulou, P., Aid, S.G., Optimal communication algorithms on star graphs using spanning tree constructions, Journal of Parallel and Distributed Computing 24, 1995, 55–71.
Fragopoulou, P., Akl, S.G., Fault tolerant communication algorithms on the star network using disjoint paths, Proceedings of the Hawaii International Conference on System Sciences 2, 1995, 5–13.
Fragopoulou, P., Akl, S.G., A framework for optimal communication on a subclass of Cayley graph based networks, Proc. of the International Conference on Computers and Communications, 1995, 241–248.
Fragopoulou, P., Akl, S.G., Efficient algorithms for global data communication on the multidimensional torus network, Proc. of the International Parallel Processing Symposium, 1995, 324–330.
Fragopoulou, P., Akl, S.G., Edge-disjoint spanning trees on the star network with applications to fault tolerance, IEEE Transactions on Computers 45, 1996, 174–185.
Fragopoulou, P., Akl, S.G., Meijer, H., Optimal communication primitives on the generalized hypercube network, Journal of Parallel and Distributed Computing 32, 1996, 173–187.
Gewali, L.P., Stojmenovie, I., Computing external watchman routes on PRAM, BSR, and interconnection models of parallel computation, Parallel Processing Letters 4, 1994, 83–93.
Goodrich, M.T., Parallel algorithms in geometry, J.E. Goodman, J. O’Rourke (eds.), Discrete and Computational Geometry, CRC Press, New York, 1997, 669–681.
Gordon, D.M., Parallel sorting on Cayley graphs, Algorithmica 6, 1991, 554–564.
Hamdi, M., Communications in optically interconnected computer systems, D.F. Hsu, A.L. Rosenberg, D. Sotteau (eds.), Interconnection Networks and Mapping and Scheduling Parallel Computations, DI-MACS Series in Discrete Mathematics and Theoretical Computer Science 21, 1995, 181–200.
Hatcher, P.J., Quinn, M.J., Data-Parallel Programming on MIMD Computers, MIT Press, Cambridge, Massachusetts, 1991.
Hillis, W.D., The Connection Machine, MIT Press, Cambridge, Massachusetts, 1985.
JAJA, J., An Introduction to Parallel Algorithms, Addison-Wesley, Reading, Massachusetts, 1992.
Jwo, J.S., Lakshmivarahan, S., Dhall, S.K., Embedding of cycles and grids in star graphs, Proc. of the IEEE Symposium on Parallel and Distributed Processing, 1990, 540–547.
Karp, R.M., Ramachandran, V., A survey of parallel algorithms for shared memory machines, Vol. A, J. van Leeuwen (ed.) Handbook of Theoretical Computer Science, Elsevier, Amsterdam, 1990, 869–941.
Knu73] Knuth, D.E. The Art of Computer Programming 3, Addison-Wesley, Reading, Massachusetts, 1973.
Kruskal, C.P., Rudolph, L., Snir, M., The power of parallel prefix, IEEE Transactions on Computers 34, 1985, 965–968.
Kruskal, C.P., Rudolph, L., Snir, M., Efficient parallel algorithms for graph problems, Algorithmica 5, 1990, 43–64.
Kumar, V., Grama, A., Gupta, A., Karypis, G., Introduction to Parallel Computing, Benjamin-Cummings, Menlo Park, California, 1994.
Kunde, M., Optimal sorting on multi-dimensionally mesh-connected computers, Proc. of the Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science No. 247, Springer-Verlag, Berlin, 1987, 408–419.
Lakshmivarahan, S., Dhall, S.K., Parallel Computing Using the Prefix Problem, Oxford University Press, New York, 1994.
Leighton, F.T., Introduction to Parallel Algorithms and Architectures, Morgan Kaufmann, San Mateo, California, 1992.
Lin, R., Olariu, S., A simple optimal parallel algorithm to solve the lowest common ancestor problem, Proc. of the International Conference on Computing and Information, Lecture Notes in Computer Science, No. 497, Springer-Verlag, Berlin, 1991, 455–461.
Luccio, F., Pagli, L., The p-shovelers problem (computing with timevarying data), SIGACT News 23, 1992, 72–75.
Luccio, F., Pagli, L., The p-shovelers problem (computing with timevarying data), Proc. of the IEEE Symposium on Parallel and Distributed Processing, 1992, 188–193.
Luccio, F., Pagli, L., Pucci, G., Three non conventional paradigms of parallel computation, Proc. of the Heinz Nixdorf Symposium, Lecture Notes in Computer Science, No. 678, Springer-Verlag, Berlin, 1992, 166–175.
Marberg, J.M., Gafni, E., Sorting in constant number of row and column phases on a mesh, Algorithmica 3, 1988, 561–572.
Melter, R.A., Stojmenovie, I., Solving city block metric and digital geometry problems on the BSR model of parallel computation, Journal of Mathematical Imaging and Vision 5, 1995, 119–127.
Menn, A., Somani, A.K., An efficient sorting algorithm for the star graph interconnection network, Proc. of the International Conference on Parallel Processing 3, 1990, 1–8.
Mulmuley, K., Computational Geometry: An Introduction through Randomized Algorithms, Prentice Hall, Englewood Cliffs, New Jersey, 1993.
Nigam, M., Sahni, S., Sorting n numbers on n x n reconfigurable meshes with buses, Journal of Parallel and Distributed Computing 23, 1994, 37–48.
Nigam, M., Sahni, S., Krishnamurthy, B., Embedding Hamiltonians and hypercubes in star interconnection graphs, Proc. of the International Conference on Parallel Processing 3, 1990, 340–343.
O’Rourke, J., Computational Geometry in C, Cambridge University Press, Cambridge, England, 1994.
Pavel, S., Computation and Communication Aspects of Arrays with Optical Pipelined Buses, Ph.D. thesis, Department of Computing and Information Science, Queen’s University, Kingston, Ontario, 1996.
Pavel, S., AU, S.G., Matrix operations using arrays with reconfigurable optical buses, Journal of Parallel Algorithms and Applications 8, 1996, 223–242.
Pavel, S., Aid, S.G., Area-time trade-offs in arrays with optical pipelined buses, Applied Optics 35, 1996, 1827–1835.
Pavel, S., Aid, S.G., On the power of arrays with reconfigurable optical buses, Proc. of the International Conference on Parallel and Distributed Processing Techniques and Applications, 1996, 1443–1454.
Pavel, S., Aid, S.G., Efficient algorithms for the Hough transform on arrays with reconfigurable optical buses, Proc. of the International Parallel Processing Symposium, 1996, 697–701.
Pavel, S., Aid, S.G., Integer sorting and routing in arrays with reconfig-urable optical buses, to appear in International Journal of Foundations of Computer Science, Special Issue on Interconnection Networks, 1998.
Prasanna Kumar, V.K., Raghavendra, C.S., Array processor with multiple broadcasting, Journal of Parallel and Distributed Computing 4, 1987, 173–190.
Preparata, F.P., Shamos, M.I., Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
Preparata, F.P., Vuillemin, J.E., The cube-connected cycles: A versatile network for parallel computation, Communications of the ACM 24, 1981, 300–309.
Qiu, K., The Star and Pancake Interconnection Networks: Properties and Algorithms, Ph.D. Thesis, Department of Computing and Information Science, Queen’s University, Kingston, Ontario, 1992.
Qiu, K., Ald, S.G., Load balancing, selection and sorting on the star and pancake interconnection networks, Parallel Algorithms and Applications 2, 1994, 27–42.
Qiu, K., Aid, S.G., On some properties of the star graph, Journal of VLSI Design, Special Issue on Interconnection Networks 2, 1994, 389–396.
Qiu, K., Aid, S.G., Parallel point location algorithms on hypercubes, Proc. of the Tenth International Conference on Parallel and Distributed Computing, 1997, 27–30.
Qiu, K., Aid, S.G., Meijer, H., On some properties and algorithms for the star and pancake interconnection networks, Journal of Parallel and Distributed Computing 22, 1994, 16–25.
Qiu, K., Meijer, H., Aid, S.G., Parallel routing and sorting on the pancake network, Proc. of the International Conference on Computing and Information, Lecture Notes in Computer Science, No. 497, Springer-Verlag, Berlin, 1991, 360–371.
Qiu, K., Meijer, H., Aid, S.G., Decomposing a star graph into disjoint cycles, Information Processing Letters 39, 1991, 125–129.
Qiu, K., Meijer, H., Aid, S.G., On the cycle structure of star graphs, Congressus Numerantium 96, 1993, 123–141.
Rajasekaran, S., Wei, D.S.L., Selection, routing and sorting on the star graph, Proc. of the International Parallel Processing Symposium, 1993, 661–665.
Rajasekaran, S., Wei, D.S.L., Selection, routing, and sorting on the star graph, Journal of Parallel and Distributed Computing 41, 1997, 225–233
Ranka, S., Salmi, S., Hypercube Algorithms, Springer-Verlag, New York, 1990.
Reif, J.H. (ed.), Synthesis of Parallel Algorithms, Morgan Kaufmann, San Mateo, California, 1993.
SSS86] Scherson, I. Sen, S., Shamir, A., Shear-sort: A true two-dimensional sorting technique for VLSI networks, Proc. of the International Conference on Parallel Processing,1986, 903–908.
Seitz, C.L., Concurrent VLSI architectures, IEEE Transactions on Computers 33, 1984, 1247–1265.
Seitz, C.L., The cosmic cube, Communications of the ACM 28, 1985, 22–33.
Semé, D., Myoupo, J.-F., A parallel solution of the sequence alignment problem using BSR model, Proc. of the International Conference on Parallel and Distributed Computing, 1997, 357–362.
Snir, M., Depth-size tradeoffs for parallel prefix computation, Journal of Algorithms 7, 1986, 185–201.
Springsteel, F., Stojmenovie, I., Parallel general prefix computations with geometric, algebraic and other applications, International Journal of Parallel Programming 18, 1989, 485–503.
Stojmenovié, I., Constant time BSR solutions to parenthesis matching, tree decoding, and tree reconstruction from its traversals, IEEE Transactions on Parallel and Distributed Systems 7, 1996, 218–224.
Sto83] Stout, Q.F., Mesh-connected computers with broadcasting IEEE Transactions on Computers 32 1983, 826–830.
Sur, S., Srimani, P.K., A fault tolerant routing algorithm in star graphs, Proc. of the International Conference on Parallel Processing 3, 1991, 267–270.
Tarjan, R.E., Vishkin, U., An efficient parallel biconnectivity algorithm, SIAM Journal of Computing 14, 1985, 862–874.
Trew, A., Wilson, G. (eds.), Past, Present, Parallel, Springer-Verlag, Berlin, 1991.
Ullman, J.D., Computational Aspects of VLSI, Computer Science Press, Rockville, Maryland, 1984.
Vishkin, U., A parallel-design distributed implementation (PDDI) general-purpose computer, Theoretical Computer Science 32, 1984, 157–172.
Vishkin, U., On efficient parallel strong orientation, Information Processing Letters 20, 1985, 235–240.
Wagner, W., Han, Y., Parallel algorithms for bucket sorting and data dependent prefix problems, Proc. of the International Conference on Parallel Processing, 1986, 924–930.
Wyllie, J.C., The Complexity of Parallel Computations, Ph.D. Thesis, Department of Computer Science, Cornell University, Ithaca, New York, 1979.
Xiang, L., Ushijima, K., ANSV problem on BSRs, Information Pro- cessing Letters 65, 1998, 135–138.
Xiang, L., Ushijima, K., Decoding and drawing on BSR for a binary tree from its i - p sequence, to appear in Parallel Processing Letters, 1999.
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Akl, S.G. (2000). The Design of Efficient Parallel Algorithms. In: Błażewicz, J., Ecker, K., Plateau, B., Trystram, D. (eds) Handbook on Parallel and Distributed Processing. International Handbooks on Information Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04303-5_2
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