CmpE 511 Presentation Definition and Analysis of a Class of Spanning Bus Orthogonal Multiprocessing...

CmpE 511 Presentation

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 Orthogonal Shared Memory

Multiprocessors Conclusion


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.


Introduction (II) The access rule:

Pk accesses Mij

if k= i for all j ( By rows )

or k= j for all i ( By columns )


Introduction (III)

Binary Access Rule

Generalized Acces Mode in q


Orthogonal Graphs

Definitions Degree Connectivity Diameter


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


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

!


Definitions (III)

N(q) is the number of nearest neighbours under mode q


Degree of OG

D= (2^(m-n)-1)*#Q*. If Q* is disjoint set of modes.


Connectivity


Diameter


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


Omega Graph Examples

The graph of 4G(3,4) . Hypercube


Omega Graphs

The Graph of 2 G ( 2 , 4 )


Spanning Buses

Transformation of a fully connected face into spanning bus

Spanning bus graph for2 G ( 2 ,4 , { 0 , 2 })


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)


MDA Example

MDA Example

2 G ( 2 ,4 , { 0 ,1 , 2 ,3})


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.


Any questions ?

Thanks!!!

CmpE 511 Presentation Definition and Analysis of a Class of Spanning Bus Orthogonal Multiprocessing...

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