CmpE 511 Presentation Definition and Analysis of a Class of Spanning Bus Orthogonal Multiprocessing...
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Transcript of 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
CmpE 511 Presentation
Contents
Introduction Orthogonal Graphs The Class Of Omega Graphs Orthogonal Shared Memory
Multiprocessors Conclusion
CmpE 511 Presentation
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
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
Introduction (III)
Binary Access Rule
Generalized Acces Mode in q
CmpE 511 Presentation
Orthogonal Graphs
Definitions Degree Connectivity Diameter
CmpE 511 Presentation
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
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
Definitions (III)
N(q) is the number of nearest neighbours under mode q
CmpE 511 Presentation
Degree of OG
D= (2^(m-n)-1)*#Q*. If Q* is disjoint set of modes.
CmpE 511 Presentation
Connectivity
CmpE 511 Presentation
Diameter
CmpE 511 Presentation
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
Omega Graph Examples
The graph of 4G(3,4) . Hypercube
CmpE 511 Presentation
Omega Graphs
The Graph of 2 G ( 2 , 4 )
CmpE 511 Presentation
Spanning Buses
Transformation of a fully connected face into spanning bus
Spanning bus graph for2 G ( 2 ,4 , { 0 , 2 })
CmpE 511 Presentation
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
MDA Example
MDA Example
2 G ( 2 ,4 , { 0 ,1 , 2 ,3})
CmpE 511 Presentation
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
Any questions ?
Thanks!!!