Time-Efficient Maze Routing Algorithms on Reconfigurable Mesh Architectures

The routing problem is one of the most widely studied problems in VLSI design. Maze-routing algorithms are used in VLSI routing and robot path planning. Efficiency of the parallel maze routing algorithms which were mostly based on C. Y. Lee's algorithm8is poor. In this paper, we propose time-efficient algorithms to solve the maze-routing problem on a reconfigurable mesh architecture. The constant-time algorithms presented include: (i) testing the existence of specific types of paths between two terminals, and (ii) finding an absolute shortest path (ASP) and a shortest duplex-path (SDP). In addition, a fast algorithm to find the single shortest path (SSP) is presented. The simulation results indicate that a large percentage of the shortest paths that exist between two randomly selected terminals fall into one of the categories studied in this paper.

[1]  Niel K. Madsen,et al.  Matrix Multiplication by Diagonals on a Vector/Parallel Processor , 1976, Inf. Process. Lett..

[2]  M. H. Schultz,et al.  Topological properties of hypercubes , 1988, IEEE Trans. Computers.

[3]  C. Thomborson,et al.  Area-time complexity for VLSI , 1979, STOC.

[4]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[5]  Arnold L. Rosenberg,et al.  On Embedding Rectangular Grids in Square Grids , 1982, IEEE Transactions on Computers.

[6]  Sartaj Sahni,et al.  Maze Routing on a Hypercube Multiprocessor Computer , 1987, International Conference on Parallel Processing.

[7]  C. Y. Lee.  An Algorithm for Path Connections and Its Applications , 1961, IRE Trans. Electron. Comput..

[8]  Massimo Maresca,et al.  Polymorphic-Torus Network , 1989, IEEE Trans. Computers.

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

[10]  Gen-Huey Chen,et al.  Constant Time Algorithms for the Transitive Closure and Some Related Graph Problems on Processor Arrays with Reconfigurable Bus Systems , 1990, IEEE Trans. Parallel Distributed Syst..

[11]  C. Thomborson,et al.  A Complexity Theory for VLSI , 1980 .

[12]  A. George.  Nested Dissection of a Regular Finite Element Mesh , 1973 .

[13]  Ilse C. F. Ipsen,et al.  How to Embed Trees in Hypercubes. , 1985 .

[14]  S. Lennart Johnsson,et al.  Solving narrow banded systems on ensemble architectures , 1985, TOMS.

[15]  Lennart Johnsson.  Computational Arrays for Band Matrix Equations , 1981 .

[16]  A. Nijenhuis.  Combinatorial algorithms , 1975 .

[17]  Sartaj Sahni,et al.  Parallel Matrix and Graph Algorithms , 1981, SIAM J. Comput..

[18]  Charles L. Seitz,et al.  The cosmic cube , 1985, CACM.

[19]  J. O. Eklundh,et al.  A Fast Computer Method for Matrix Transposing , 1972, IEEE Transactions on Computers.

[20]  David J. Kuck,et al.  A Survey of Parallel Machine Organization and Programming , 1977, CSUR.

[21]  Harold S. Stone,et al.  A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations , 1973, IEEE Transactions on Computers.

[22]  Uri C. Weiser,et al.  Towards a Formal Treatment of VLSI Arrays , 1981 .

[23]  I. H. Öğüş,et al.  NATO ASI Series , 1997 .

[24]  Harold S. Stone,et al.  Parallel Processing with the Perfect Shuffle , 1971, IEEE Transactions on Computers.

[25]  Farokh B. Bastani,et al.  Strategies for mapping Lee's maze routing algorithm onto parallel architectures , 1993, [1993] Proceedings Seventh International Parallel Processing Symposium.

[26]  Ralph Grishman,et al.  The NYU Ultracomputer—Designing an MIMD Shared Memory Parallel Computer , 1983, IEEE Transactions on Computers.

[27]  B. Box.  Field programmable gate array based reconfigurable preprocessor , 1994, Proceedings of IEEE Workshop on FPGA's for Custom Computing Machines.

[28]  Tahsin M. Kurç,et al.  Parallelization of Lee's Routing Algorithm on a Hypercube Multicomputer , 1991, EDMCC.

[29]  Roy M. Jenevein,et al.  Scaleability of a Binary Tree on a Hypercube , 1986, ICPP.

[30]  David Peleg,et al.  The Power of Reconfiguration , 1991, J. Parallel Distributed Comput..

[31]  Sl Johnsson.  Pipelined Linear Equation Solvers and VLSI , 1982 .

[32]  Michael J. Flynn,et al.  Very high-speed computing systems , 1966 .

[33]  Lynn Elliot Cannon,et al.  A cellular computer to implement the kalman filter algorithm , 1969 .

[34]  Dionysios I. Reisis,et al.  Parallel Computations on Reconfigurable Meshes , 1993, IEEE Trans. Computers.

[35]  Charles E. Leiserson,et al.  Area-Efficient Graph Layouts (for VLSI) , 1980, FOCS.

[36]  F. Gustavson,et al.  Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine , 1984 .

[37]  Lennart Johnsson,et al.  Combining Parallel and Sequential Sorting on a Boolean n–cube , 1984 .

[38]  Sartaj Sahni,et al.  Reconfigurable Mesh Algorithms For Fundamental Data Manipulation Operations , 1993 .