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Questions and Answers
What was the world's record for matrix multiplication complexity in terms of big-O notation?
What was the world's record for matrix multiplication complexity in terms of big-O notation?
- O(n^2.37548) (correct)
- O(n^2.81)
- O(n^2.37293)
- O(n^2+ε)
Who achieved a new record for matrix multiplication complexity by reducing it from 2.37548 to 2.37293?
Who achieved a new record for matrix multiplication complexity by reducing it from 2.37548 to 2.37293?
- Alman and Williams
- Jacob Scott
- Coppersmith & Winograd
- Virginia Vassilevska Williams (correct)
What did Lebeck mention as a possible extension for the communication lower bound?
What did Lebeck mention as a possible extension for the communication lower bound?
- Ω(n^2.81 / M^0.4) (correct)
- Ω(n^2.37548)
- Ω(n log^2 7 / M(log^2 7)/2 – 1)
- Ω(n^2+ε)
Who suggested the possibility of an O(n^2+ε) algorithm?
Who suggested the possibility of an O(n^2+ε) algorithm?
Which algorithm reduced the world's record of matrix multiplication complexity to 2.37286?
Which algorithm reduced the world's record of matrix multiplication complexity to 2.37286?
What is the main focus of the given text?
What is the main focus of the given text?
In the context of the text, what does 'Ax=b' refer to?
In the context of the text, what does 'Ax=b' refer to?
What is a key factor in determining the number of words moved according to the General Communication Lower Bound Thm?
What is a key factor in determining the number of words moved according to the General Communication Lower Bound Thm?
What type of linear program is used to minimize the value of sHBL in the General Communication Lower Bound Thm?
What type of linear program is used to minimize the value of sHBL in the General Communication Lower Bound Thm?
What is the role of projections φj in determining the Communication Lower Bound Thm?
What is the role of projections φj in determining the Communication Lower Bound Thm?
Which recent mathematical result is crucial for proving the General Communication Lower Bound Thm?
Which recent mathematical result is crucial for proving the General Communication Lower Bound Thm?
What is the main focus of the lecture on 'Applications of Parallel Computing'?
What is the main focus of the lecture on 'Applications of Parallel Computing'?
In the context of communication lower bound, what is referred to as the most expensive operation?
In the context of communication lower bound, what is referred to as the most expensive operation?
For the n-body algorithm, what does the term 'array of structures' refer to?
For the n-body algorithm, what does the term 'array of structures' refer to?
In the context of n-body data access, what does 'access A(3), B(5)' imply?
In the context of n-body data access, what does 'access A(3), B(5)' imply?
What is the maximum number of loop iterations that can be done if only 10 entries of A(i) and B(j) can be accessed?
What is the maximum number of loop iterations that can be done if only 10 entries of A(i) and B(j) can be accessed?
What is the purpose of optimizing tiling in the usual n-body algorithm?
What is the purpose of optimizing tiling in the usual n-body algorithm?
'Optimal tiling (M=10)' in the usual n-body algorithm involves reading how many entries of A and B?
'Optimal tiling (M=10)' in the usual n-body algorithm involves reading how many entries of A and B?
'C = A*B' in the context of linear algebra represents what operation?
'C = A*B' in the context of linear algebra represents what operation?
'Communication Lower Bound on C = AꞏB' focuses on minimizing communication by limiting access to how many entries of A, B, and C in cache?
'Communication Lower Bound on C = AꞏB' focuses on minimizing communication by limiting access to how many entries of A, B, and C in cache?
'# loop iterations doable with M words of data' is represented by which formula in the context of communication lower bound?
'# loop iterations doable with M words of data' is represented by which formula in the context of communication lower bound?
What is the purpose of synchronization in parallel computing, as mentioned in the text?
What is the purpose of synchronization in parallel computing, as mentioned in the text?
In the context of parallel computing, what does the term 'critical region' refer to?
In the context of parallel computing, what does the term 'critical region' refer to?
What does the OpenMP directive 'barrier' primarily facilitate in parallel computing?
What does the OpenMP directive 'barrier' primarily facilitate in parallel computing?
What does 'Mutual exclusion' aim to achieve in parallel computing?
What does 'Mutual exclusion' aim to achieve in parallel computing?
What role does 'omp_get_thread_num()' play in achieving synchronization in parallel computing?
What role does 'omp_get_thread_num()' play in achieving synchronization in parallel computing?
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