By Cheng-Zhong Xu, Francis C.M. Lau
Load Balancing in Parallel pcs: thought and perform is ready the fundamental software program means of load balancing in allotted reminiscence message-passing parallel desktops, also known as multicomputers. each one processor has its personal tackle house and has to converse with different processors via message passing. normally, a direct, point-to-point interconnection community is used for the communications. Many advertisement parallel pcs are of this type, together with the Intel Paragon, the pondering laptop CM-5, and the IBM SP2. Load Balancing in Parallel pcs: concept and perform offers a complete therapy of the topic utilizing rigorous mathematical analyses and functional implementations. the point of interest is on nearest-neighbor load balancing equipment during which each processor at each step is particular to balancing its workload with its direct neighbours simply. Nearest-neighbor equipment are iterative in nature simply because a world balanced country should be reached via processors' successive neighborhood operations. considering nearest-neighbor tools have a particularly cozy requirement for the unfold of neighborhood load info around the approach, they're versatile when it comes to permitting one to manage the balancing caliber, potent for conserving conversation locality, and will be simply scaled in parallel desktops with a right away verbal exchange community. Load Balancing in Parallel pcs: concept and perform serves as an exceptional reference resource and will be used as a textual content for complicated classes at the topic.
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Additional resources for Load balancing in parallel computers: theory and practice
For the structures of chain, ring,mesh and torus, they derived the optimal exchange parameters that would lead to the fastestconvergence . Boillatpresented a version of the dimension exchange method (ca[ledCayley diffusion) in ,in which he derived the optimal exchange parameters for Cayley graphs. The D E algorithm discussed above is based on a priori edge-coloring of system graphs. The edge-coloring is deterministic in the sense that the colors of incident edges of a node are determined by the system graph.
Suppose A = 1. Then E is a permutation matrix because for all 1 < c < n, Ee is a permutation matrix. Therefore, E has the eigenvalue 1 in modulus with multiplicity N w h e n A = 0 or 1, and hence 7(E) = 1. Thus, limt-,~o E t does not exist or if it exists, does not converge to ~. Consequently, l i m t _ ~ E t = ~ if and only if A E (0, 1). (2) Since limt-~o E t = E--,for any initial workload distribution W °, we have lira W t~ = ~ W ° = b W t--~ 42 3. T H E G D E M E T H O D where b = ~I<~ S ~ a r convergence resulCs ~ ~ e sCatic w o r ~ o a d model were ob[a~ed ~dependenfly b y Boilla¢ ef al. [17, 18]. Moreove5 Bo~a¢ ef al. derived ~ upper b o ~ d O(N ~) for ~ e convergence fac[or of ~ e dff~sion m e ~ o d , where N is ~ e n ~ b e r of processors. ~ a ¢ is, load b a l ~ c ~ g w i ~ ~ e dff~sion m e ~ o d w ~ convergence to ~ eq~bri~ sCa~e~ p o l ~ o ~ a l ~ e . S u b r ~ ~ d S ~ e r s o n derived lower ~ d upper b o n d s on ~ e ~ g ~ e of ~ e dff~sion m e ~ o d ~ arb9 ~ a ~ n e ~ o r ~ .
S ~ a r convergence resulCs ~ ~ e sCatic w o r ~ o a d model were ob[a~ed ~dependenfly b y Boilla¢ ef al. [17, 18]. Moreove5 Bo~a¢ ef al. derived ~ upper b o ~ d O(N ~) for ~ e convergence fac[or of ~ e dff~sion m e ~ o d , where N is ~ e n ~ b e r of processors. ~ a ¢ is, load b a l ~ c ~ g w i ~ ~ e dff~sion m e ~ o d w ~ convergence to ~ eq~bri~ sCa~e~ p o l ~ o ~ a l ~ e . S u b r ~ ~ d S ~ e r s o n derived lower ~ d upper b o n d s on ~ e ~ g ~ e of ~ e dff~sion m e ~ o d ~ arb9 ~ a ~ n e ~ o r ~ .