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- Parallel computers
- Types of parallel computers
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Parallel execution time, Time complexity, Debugging and evaluating parallel programs , Embarrassingly parallel computations.
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Embarrassingly parallel examples, Geometrical transformations of images
- Finite differences
- Pair wise interactions
- Search – it creates tasks dynamically during execution of the program.
- Parameter study – it has fixed number of tasks where different task performs different functions.
- Scan (prefix sums) : It takes a binary associative operator & an array and on processing it returns a new array in which each element of new array has sum of all previous elements.
- List ranking : It takes a linked list & defines the position of each element in the list.
- Sorting: there are various sorting algorithm like quick sort, insertion sort, selection sort.
- String matching
- Parallel algorithms on trees and graphs
- Connected components problem: it takes an undirected graph as an input. It returns components that are connected by an edge. This can be achieved using breadth-first-search or depth-first-search.
- Shortest path algorithm: they are mainly used to calculate the shortest distance between two different nodes.
- Convex hull
- Closest pairs
- Delaunay triangulation
- Fourier transform, Dense matrix operations, Sparse matrix operations, N-body code, Critical paths, work and span, and the relation to Amdahl’s law (cross-reference SF/Performance) Speed-up and scalability Naturally (embarassingly) parallel algorithms Parallel algorithmic patterns (divide-and-conquer, map and reduce, others) Specific algorithms (e.g., parallel MergeSort).
- Parallel graph algorithms (e.g., parallel shortest path, parallel spanning tree) (cross-reference AL/Algorithmic Strategies/Divide-and-conquer) Producer-consumer and pipelined algorithms Define “critical path”, “work”, and “span” work and span, critical path , parallel execution diagram speed-up ,algorithm’s scalability ,independent tasks , naturally parallelized.
- Parallel divide-and-conquer and/or graph algorithm and empirically sequential analog ,via map and reduce operations , producer-consumer paradigm , pipelining ,parallelization ,producer-consumer algorithms mechanisms , addressing.
- Mandelbrot set, Monte carlo methods, Partitioning and divide-and-conquer strategies, Divide-and-conquer examples, Sorting using bucket sort, Numerical integration, N-body problem, Pipelined computations, Computing platform for pipelined applications, Adding numbers, Sorting numbers, Prime number generation, Solving a system of linear equations
- Synchronous computations, Barrier and implementations, Local synchronization, Deadlock, Synchronized computations, Data parallel computations, Synchronous iteration, Solving a system of linear equations by iteration
- Heat distribution problem, Cellular automata, Load balancing and termination detection, Dynamic load balancing, Distributed termination detection algorithms, Programming with shared memory, Specifying parallelism, Sharing data
- Language constructs for parallelism, Dependency analysis, Shared data in systems with caches, Algorithms and applications, Sorting algorithms, Rank sort, Bubble sort and odd-even transposition sort, Two-dimensional sorting
- Mergesort, Quicksort, Odd-even mergesort, Bitonic mergesort, Numerical algorithms, Matrix addition, Matrix and matrix-vector multiplication, Relationship of matrices to linear equations, Implementing matrix multiplication, Direct implementation, Recursive implementation, Mesh implementation, Solving a system of linear equations linear equations
- Gaussian elimination parallel implementation, Iterative methods, Jacobi iteration, Faster convergence methods, Image processing, Low-level image processing, Smoothing, Sharpening,, Noise reduction, Mean, Median, Weighted masks
- Edge detection, Edge detection masks, The hough transform, Transformation into the frequency domain, Discrete fourier transform, Fast fourier transform, Searching and optimization, Branch-and-bound search, Genetic algorithms, Hill climbing,
- Performance metrics, scalability and overheads, Classification of algorithms, architectures and applications: searching, divide and conquer, data parallel. Static and dynamic, message passing and shared memory, systolic, Sorting and searching algorithms: mergesort, quicksort and bitonic sort, implementation on different architectures. Parallel depth-first and breadth-first search techniques.
- Matrix algorithms: striping and partitioning, matrix multiplication, linear equations, eigenvalues, dense and sparse techniques, finite element and conjugate gradient methods, Optimisation: graph problems, shortest path and spanning trees. Dynamic programming, knapsack problems, scheduling. element methods, Synthesis of parallel algorithms: algebraic methods, pipelines, homomorphisms.
COM S 526 Introduction to Parallel Algorithms and Programming:
- Models of parallel computation
- performance measures
- basic parallel constructs
- communication primitives
- parallel programming using MPI
- parallel algorithms
- matrix tree
- graph problems
- fast Fourier transforms