A theory of decomposition into prime factors of layered interconnection networks

The cross-product technique, introduced by Even and Litman (1992) [8], is extended into a full decomposition theory enabling a unique (up to isomorphism) and polynomial factorization of layered interconnection networks (including many well-known networks) into a product of prime factors. A polynomial algorithm is provided for checking whether a given layered interconnection network is isomorphic to a network that is uniquely decomposable into prime factors.

[1]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[2]  Marc Snir,et al.  A Unified Theory of Interconnection Network Structure , 1986, Theor. Comput. Sci..

[3]  Charles E. Leiserson,et al.  Fat-trees: Universal networks for hardware-efficient supercomputing , 1985, IEEE Transactions on Computers.

[4]  Wilfried Imrich,et al.  Recognizing Cartesian products in linear time , 2007, Discret. Math..

[5]  Qing Hu,et al.  Topologies of Combined (2logN - 1)-Stage Interconnection Networks , 1997, IEEE Trans. Computers.

[6]  Jean-Michel Fourneau,et al.  A graph theoretical approach to equivalence of multistage interconnection networks , 1989, Discret. Appl. Math..

[7]  Abraham Waksman,et al.  A Permutation Network , 1968, JACM.

[8]  Tse-Yun Feng,et al.  On a Class of Multistage Interconnection Networks , 1980, IEEE Transactions on Computers.

[9]  Kenneth E. Batcher,et al.  Sorting networks and their applications , 1968, AFIPS Spring Joint Computing Conference.

[10]  Eli Upfal,et al.  An O(log N) deterministic packet-routing scheme , 1992, JACM.

[11]  Frank Thomson Leighton,et al.  Parallel Computation Using Meshes of Trees , 1983, WG.

[12]  Shimon Even,et al.  Layered cross product&mdashA technique to construct interconnection networks , 1997 .

[13]  Duncan H. Lawrie,et al.  Access and Alignment of Data in an Array Processor , 1975, IEEE Transactions on Computers.

[14]  Walter Ledermann,et al.  Introduction to the theory of finite groups , 1949 .

[15]  Marshall C. Pease,et al.  The Indirect Binary n-Cube Microprocessor Array , 1977, IEEE Transactions on Computers.

[16]  Kyungsook Y. Lee.  On the Rearrangeability of 2(log2N) - 1 Stage Permutation Networks , 1985, IEEE Trans. Computers.

[17]  Annalisa Massini,et al.  Efficient algorithms for checking the equivalence of multistage interconnection networks , 2004, J. Parallel Distributed Comput..

[18]  V. Benes.  Permutation groups, complexes, and rearrangeable connecting networks , 1964 .

[19]  Jon Louis Bentley,et al.  Quad trees a data structure for retrieval on composite keys , 1974, Acta Informatica.

[20]  Shimon Even,et al.  Layered cross product—a technique to construct interconnection networks , 1992, SPAA '92.

[21]  Wilfried Imrich,et al.  Local Algorithms for the Prime Factorization of Strong Product Graphs , 2009, Math. Comput. Sci..

[22]  Tse-Yun Feng,et al.  Data Manipulating Functions in Parallel Processors and Their Implementations , 1974, IEEE Transactions on Computers.

[23]  Wilfried Imrich,et al.  Fast recognition of classes of almost-median graphs , 2007, Discret. Math..