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Definition and Analysis of a Class of Spanning Bus Orthogonal Multiprocessing Systems

Definition and Analysis of a Class of Spanning Bus Orthogonal Multiprocessing Systems. Isaac D.Scherson Department of Elecetrical Engineering Princeton University Princeton New Jersey 08544 Presentation Prepared by Dindar Öz. Contents. Introduction Orthogonal Graphs The Class Of Omega Graphs

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Definition and Analysis of a Class of Spanning Bus Orthogonal Multiprocessing Systems

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  1. Definition and Analysis of a Class of Spanning Bus Orthogonal Multiprocessing Systems Isaac D.Scherson Department of Elecetrical Engineering Princeton University Princeton New Jersey 08544 Presentation Prepared by Dindar Öz CmpE 511 Presentation

  2. Contents • Introduction • Orthogonal Graphs • The Class Of Omega Graphs • Orthogonal Shared Memory Multiprocessors • Conclusion CmpE 511 Presentation

  3. Introduction (I) • p Processors access p*p memory modules • First applied to some vector processing problems • Because the acces is orthogonal the system named Orthogonal Multi-Processor or OMP for short. CmpE 511 Presentation

  4. Introduction (II) • The access rule:Pk accesses Mij if k= i for all j ( By rows ) or k= j for all i ( By columns ) CmpE 511 Presentation

  5. Introduction (III) Binary Access Rule Generalized Acces Mode in q CmpE 511 Presentation

  6. Orthogonal Graphs • Definitions • Degree • Connectivity • Diameter CmpE 511 Presentation

  7. Definitions (I) • Ym : set of all binary vectors of length m • Q = {0,1,2,.....m-1} ordered set • + is bitvise ex-OR and * is defined CmpE 511 Presentation

  8. Definitions (II) Inner Product of q Orthogonal Mode of q ! Two vectors are orthogonal if and only if they match on n bits starting at bit position q CmpE 511 Presentation

  9. Definitions (III) N(q) is the number of nearest neighbours under mode q CmpE 511 Presentation

  10. Degree of OG • D= (2^(m-n)-1)*#Q*. If Q* is disjoint set of modes. CmpE 511 Presentation

  11. Connectivity CmpE 511 Presentation

  12. Diameter CmpE 511 Presentation

  13. Omega Graphs • A Connected orthogonal graph with disjoint sets of modes requires that we choose m and n suc that for some integer w>=2 m= w(m-n) or m=wm/(w-1). Q* is such that for all q(i) and q(i+1) in Q* q(i+1) - q(i) mod m = m-n and #Q* = w • These graphs called w graphs wG(n,m)Example : 4 G(3,4) , 2G(2,4) • mG(m-1,m) is also called hypercube CmpE 511 Presentation

  14. Omega Graph Examples The graph of 4G(3,4) . Hypercube CmpE 511 Presentation

  15. Omega Graphs The Graph of 2 G ( 2 , 4 ) CmpE 511 Presentation

  16. Spanning Buses Transformation of a fully connected face into spanning bus Spanning bus graph for 2 G ( 2 ,4 , { 0 , 2 }) CmpE 511 Presentation

  17. Orthogonal Shared Memory Multiprocessors 2^n Processors accesse 2^m memory modules orthogonally • If graph is (n, 2n , {0,1,2,...2n-1})then the structure is called MDA(Multi-dimensional acces) • If graph is (n,2n, {0,n}) then the structure is called as OMP (Orthogonal Shared Memory Access) CmpE 511 Presentation

  18. MDA Example MDA Example 2 G ( 2 ,4 , { 0 ,1 , 2 ,3}) CmpE 511 Presentation

  19. Conclusion • Orthogonal Multiprocessing Systems provides p processors to p*p Memory modules. • The definition of orthogonal graphs is very general definition and its based on binary vector operations • Access rules in Orthogonal systems are determined by the vector orthogonality rules. • Omega Graphs , hyper cubes, OMP and MDA systems are all subsets of our general orthogonal network set. CmpE 511 Presentation

  20. Any questions ? Thanks!!! CmpE 511 Presentation

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