Outline of Material for Test #2

Parallel Collective Communication Primitives

• Be able to define One-to-All, All-to-All, scatter, gather and All-to-All Personalized communication primitives. (In other words, be able to reconstruct Figures 4.1, 4.8, 4.14, and 4.16 from the text)
• One-to-All Broadcast
• Be able to describe and analyze the Hypercube One-to-All broadcast algorithm.
• Be prepared to answer questions about the algorithms as listed in program form in Algorithm 4.1, and 4.2 from the text.
• Understand how the One-to-All broadcast algorithm can be used as a basis for performing the Single-Node Accumulation.
• Understand and be prepared to discuss the use of relabeling processor ID's using XOR to achieve the generalized algorithm
• All-to-All Broadcast
• Understand the All-to-All broadcast algorithms for the ring and Hypercube topology. In particular, pay attention to message sizes at each step of the algorithm.
• Be prepared to answer questions about the algorithms as listed in program form in Algorithm 4.4, 4.5, and 4.6 from handout.
• Be able to describe how the All-to-All broadcast can be used to as a basis for performing the Reduction or Multinode Accumulation operations.
• Know the difference between an All-to-All reduction and an All-Reduce
• One-to-All Personalized Communication
• Understand how this algorithm is a variation of the One-to-All broadcast except with shrinking message sizes.
• Be able to derive and analyze this algorithm on a Hypercube network by generalizing the One-to-All (scatter,gather) algorithm results.
• All-to-All Personalized Communications
• Be able to describe and analyze the the Hypercube algorithm.
• Be able to describe and analyze the E-cube routing algorithm.
• Be able to generalize the ts + m tw performance model to take in account network bisection width.
• Be able to describe how the all-to-all personalized algorithm relates to matrix transpose.
• Prefix-Sum algorithm
• Know what a prefix-sum is and how it is used
• Be able to describe the hypercube algorithm
• Be able to estimate running time using the ts + m tw communication cost model
• Communication optimizations
• Be able to determine if an argument is optimal based on bisection bandwidth arguments.
• Be able to discuss and analyze the optimizations of communication algorithms as described in section 4.7
• Know table 4.1 and 4.2 for the algorithms we have covered.
• Be able to derive timing measurements for any of the above algorithms!
• Study the Homework Assignments!

Performance and Scalability of Parallel Systems

• General Principles
• Speedup
• Parallel Speedup, S = t1/tp
• Ideal Speedup, S_ideal = p
• Actual Speedup, S_actual = t_best/tp = S*E_a = S_ideal*E_p*E_a
• Efficiency
• Algorithmic Efficiency, E_a = T_best/t1
• Parallel Efficiency, E_p = S/S_ideal = S/p
• System Efficiency, E = E_a*E_p
• Amdahl's Law
If a parallel algorithm consists of a fully parallel part and a fully serial part such that the fraction of instructions that are fully serial is given by f , then the speedup for this parallel algorithm can be given by:

tp = ((1-f)/p + f)*t1

In other words speedup is given by

S = 1/((1-f)/p + f).

Taking the limit as p increases to infinity gives an upper bound on speedup such that

S <= 1/f

• Be able to define Speedup, Efficiency, Cost, Cost Optimal, Problem Size, Overhead Function, and Isoefficiency Function.
• Be able to determine if an algorithm is Cost Optimal.
• Be able to determine if an algorithm has an Isoefficiency function
• Be able to derive the overhead function and use this function to determine the existence of an Isoefficiency function. Be able to show that the overhead function is related to the isoefficiency function when one exists.
• Understand why there is a lower bound on the isoefficiency function as described in section 5.4.4 from text.
• What is the degree of concurrency of a parallel algorithm?
• What is the relationship between degree of concurrency and the isoefficiency function? See section 5.4.5 from text.
• What are the sources of parallel overhead? ANS: Communication time, Load Imbalance, and additional computations performed by the parallel algorithm.
• What is scaled speedup? How do we measure it?
• What is memory and time-constrained scaled speedup? How do we measure these?
• Study the Homework Assignments!