CS855: Parallel Sorting Algorithms
Marc Moreno Maza
February 19, 2008
1
Outline
We discuss parallel deterministic sorting algorithms based on the
compare-and-exchange (CE) operation. The lower bound on the number of
CE operations to sort N elements is (N
CS855: Parallel GCD Algorithms
Marc Moreno Maza
February 19, 2008
1
Outline
Why are GCD algorithms dicult to parallelize?
Parallel GCD algorithm for integers.
GCDs of univariate polynomials.
Parallel polynomial GCD algorithms based on Linear Algebra.
CS855: Parallel machine models
Marc Moreno Maza
February 19, 2008
1
Outline
The PRAM Model.
Simulation of large PRAMs on small PRAMs.
Handling Shared Memory Access Conicts: PRAM submodels.
Comparing the Computational Power of PRAM Submodels.
2
The RAM
CS855: Parallel complexity theory
Marc Moreno Maza
February 19, 2008
1
Outline
Basic notions of sequential complexity theory.
Highly parallel feasibility and NC algorithms.
Highly parallel reduction.
P-completness.
2
Basic notions of sequential comple
CS855: Parallel Linear Algebra (I)
Marc Moreno Maza
February 19, 2008
1
Outline
Routing algorithms and switching techniques
Permutation routines in mesh-based networks
Basic matrix mapping schemes
Matrix transposition
Matrix-vector multiplication
Ma
CS855: Parallel Linear Algebra (II)
Marc Moreno Maza
February 19, 2008
1
Outline
Triangular matrices and back substitution
Tridiagonal systems and even-odd reduction
Parallel direct methods for solving SLEs
2
Triangular matrices and back substitution
L