Parallel Algorithms- Sorting and Graph
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This document discusses parallel algorithms for sorting and graph problems. It covers parallel implementations of sorting algorithms like bubble sort, quicksort, and parallel compare-exchange and compare-split operations. For graphs, it discusses parallel depth-first search by partitioning the search space, all-pairs shortest paths problems, and algorithms for sparse graphs. It also briefly mentions parallel breadth-first search and parallel best-first search.
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Divide and ConquerDr Shashikant Athawale The document discusses the divide and conquer algorithm design paradigm. It begins by defining divide and conquer as recursively breaking down a problem into smaller sub-problems, solving the sub-problems, and then combining the solutions to solve the original problem. Some examples of problems that can be solved using divide and conquer include binary search, quicksort, merge sort, and the fast Fourier transform algorithm. The document then discusses control abstraction, efficiency analysis, and uses divide and conquer to provide algorithms for large integer multiplication and merge sort. It concludes by defining the convex hull problem and providing an example input and output.
Model and Design 
Model and Design Dr Shashikant Athawale This document discusses functional and imperative models of program design. It covers features of the functional model like recursion, tail recursion, and correctness proofs. The imperative model uses variables, assignments, and control structures. Proof rules are presented for loops, goto statements, functions, and procedures. Problem solving techniques like greedy algorithms are also discussed, applying concepts to problems like the knapsack problem and Huffman coding. Specific algorithms for these problems are outlined.
Fundamental of Algorithms 
Fundamental of Algorithms Dr Shashikant Athawale This document discusses fundamentals of algorithms including:
- What algorithms are and their evolution from Persian mathematicians.
- The process of designing algorithms including defining inputs, outputs, and order of instructions.
- The need for algorithms to be correct according to their specifications and methods for confirming correctness.
- Iterative design issues such as use of loops, efficiency considerations, and estimating execution time.
- Algorithmic strategies like divide and conquer, backtracking, dynamic programming, and heuristics.
CUDA Architecture
CUDA ArchitectureDr Shashikant Athawale This document provides an overview of CUDA architecture and programming. It discusses key CUDA concepts like the host/device model, CUDA C extensions, GPU memory management, and parallel programming using CUDA threads and blocks. CUDA allows developers to speed up applications by offloading work to the GPU. It provides a scalable parallel programming model that maps threads to GPU threads to express data-level parallelism across thousands of lightweight threads for applications like high-bandwidth computing and visual computing.
Basic Communication
Basic CommunicationDr Shashikant Athawale This document discusses various communication patterns in parallel and distributed systems including one-to-all broadcast, all-to-one reduction, all-to-all broadcast and reduction, all-reduce, prefix-sum, scatter, gather, and circular shift operations. It describes how to perform these operations efficiently using techniques like recursive doubling and message splitting. Improving the performance of common communication operations can be done by splitting large messages into smaller parts and combining different patterns like scatter, all-to-all, and gather.
Parallel Processing Concepts 
Parallel Processing Concepts Dr Shashikant Athawale This document discusses parallel processing concepts including:
1. Parallel computing involves simultaneously using multiple processing elements to solve problems faster than a single processor. Common parallel platforms include shared-memory and message-passing architectures.
2. Key considerations for parallel platforms include the control structure for specifying parallel tasks, communication models, and physical organization including interconnection networks.
3. Scalable design principles for parallel systems include avoiding single points of failure, pushing work away from the core, and designing for maintenance and automation. Common parallel architectures include N-wide superscalar, which can dispatch N instructions per cycle, and multi-core which places multiple cores on a single processor socket.
Dynamic programming
Dynamic programmingDr Shashikant Athawale Dynamic programming is an algorithm design technique that solves problems by breaking them down into smaller subproblems. It is useful for problems that exhibit optimal substructure and overlapping subproblems. Some examples of problems solved using dynamic programming include the optimal binary search tree problem, the 0/1 knapsack problem, and matrix chain multiplication. Dynamic programming works by storing the results of subproblems to avoid recomputing them, building up to the overall optimal solution.
Parallel algorithms 
Parallel algorithms Dr Shashikant Athawale This document discusses parallel algorithms and models of parallel computation. It begins with an overview of parallelism and the PRAM model of computation. It then discusses different models of concurrent versus exclusive access to shared memory. Several parallel algorithms are presented, including list ranking in O(log n) time using an EREW PRAM algorithm and finding the maximum of n elements in O(1) time using a CRCW PRAM algorithm. It analyzes the performance of EREW versus CRCW models and shows how to simulate a CRCW algorithm using EREW in O(log p) time using p processors.
Greedy method 
Greedy method Dr Shashikant Athawale The document discusses greedy algorithms and how they can be applied to solve optimization problems like the knapsack problem, activity selection problem, and job sequencing problem. It provides examples of greedy algorithms for each problem. A greedy algorithm works by making locally optimal choices at each step in the hope of finding a globally optimal solution. For the knapsack problem, the greedy approach sorts items by profit/weight ratio and fills the knapsack accordingly. For activity selection, it schedules activities based on earliest finish time. For job sequencing, it sorts jobs by profit and schedules the most profitable jobs that meet deadlines.
Divide and conquer
Divide and conquerDr Shashikant Athawale The document discusses divide and conquer algorithms. It describes divide and conquer as a design strategy that involves dividing a problem into smaller subproblems, solving the subproblems recursively, and combining the solutions. It provides examples of divide and conquer algorithms like merge sort, quicksort, and binary search. Merge sort works by recursively sorting halves of an array until it is fully sorted. Quicksort selects a pivot element and partitions the array into subarrays of smaller and larger elements, recursively sorting the subarrays. Binary search recursively searches half-intervals of a sorted array to find a target value.
Branch and bound
Branch and boundDr Shashikant Athawale The branch-and-bound method is used to solve optimization problems by traversing a state space tree. It computes a bound at each node to determine if the node is promising. Better approaches traverse nodes breadth-first and choose the most promising node using a bounding heuristic. The traveling salesperson problem is solved using branch-and-bound by finding an initial tour, defining a bounding heuristic as the actual cost plus minimum remaining cost, and expanding promising nodes in best-first order until finding the minimal tour.
Asymptotic notation
Asymptotic notationDr Shashikant Athawale This document discusses asymptotic notations that are used to characterize an algorithm's efficiency. It introduces Big-Oh, Big-Omega, and Theta notations. Big-Oh gives an upper bound on running time. Big-Omega gives a lower bound. Theta gives both upper and lower bounds, representing an algorithm's exact running time. Examples are provided for each notation. Time complexity is also introduced, which describes how the time to solve a problem changes with problem size. Worst-case time analysis provides an upper bound on runtime.
String matching algorithms
String matching algorithmsDr Shashikant Athawale This document discusses and defines four common algorithms for string matching:
1. The naive algorithm compares characters one by one with a time complexity of O(MN).
2. The Knuth-Morris-Pratt (KMP) algorithm uses pattern preprocessing to skip previously checked characters, achieving linear time complexity of O(N+M).
3. The Boyer-Moore (BM) algorithm matches strings from right to left and uses pattern preprocessing tables to skip more characters than KMP, with sublinear worst-case time complexity of O(N/M).
4. The Rabin-Karp (RK) algorithm uses hashing techniques to find matches in text substrings, with time complexity of
Advanced Wireless Technologies
Advanced Wireless TechnologiesDr Shashikant Athawale This document discusses several topics related to advanced wireless technologies, including Voice over IP networks (VoIP), vehicular networks, and delay tolerant networks. It provides overviews and definitions of each topic, describing key aspects like VoIP architecture and protocols, vehicular communication methods between vehicles and infrastructure, and the store-carry-forward approach used in delay tolerant networks to allow communication in intermittent connectivity scenarios. Application examples are also given for each such as using VoIP for voice calls over the internet, safety and traffic applications in vehicular networks, and file sharing or telemedicine over delay tolerant networks.
Vo ip
Vo ipDr Shashikant Athawale VoIP allows users to make voice calls using an Internet connection instead of a regular phone line. It works by converting voice into digital data packets that are transmitted over the IP network and then reconstructed at the receiving end. The key benefits of VoIP include lower costs compared to traditional phone service, open standards that ensure interoperability between vendors, and the ability to integrate voice and data onto a single network. Common VoIP protocols are H.323, SIP, and MGCP. VoIP sees broad use for internet calling and is widely used to provide phone services at a lower cost than traditional telephone networks.
Vehicular network
Vehicular networkDr Shashikant Athawale Vehicular networks allow vehicles to communicate with each other (vehicle-to-vehicle) and with roadside infrastructure (vehicle-to-infrastructure). Vehicles act as moving nodes that form a mobile ad hoc network (MANET). Key aspects include dynamic topology, location-based routing protocols, and applications related to safety, traffic management, and infotainment. Communications can be unicast, multicast, or broadcast between vehicles and infrastructure to support functions like electronic brake lights, platooning, and traffic information systems.
Delay telerant network
Delay telerant networkDr Shashikant Athawale Delay tolerant networks (DTNs) allow communication in networks with intermittent connectivity by using a store-carry-forward approach. DTNs employ a set of protocols that store messages during network disconnections and forward them when connectivity is available. They can provide communication even when end-to-end paths do not exist. Key properties of DTNs include high latency, low data rates, disconnection, long queuing delays, short contact ranges, and dynamic topologies. Potential applications of DTNs include telemedicine in remote areas, social networking, communication under censorship, file sharing, and sharing cellular minutes.
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- 1. PARALLELALGORITHMS SORTING AND GRAPH Prof. Shashikant V. Athawale Assistant Professor | Computer Engineering Department | AISSMS College of Engineering, Kennedy Road, Pune , MH, India - 411001
- 2. Contents ❖ Issues in Sorting on Parallel Computers ❖ Bubble Sort and its Variants ❖ Parallelizing Quicksort ❖ All-Pairs Shortest Paths ❖ Algorithm for sparse graph ❖ Parallel Depth-First Search ❖ Parallel Best-First Search.
- 3. Parallel Depth First Search ❖ Depth-first search can be performed in parallel by partitioning the search space into many small, disjunct parts (subtrees) that can be explored concurrently.
- 4. Sorting ❖ Sorting can be comparison-based or non comparison- based ❖ The fundamental operation of comparison-based sorting is compare-exchange.
- 5. Sorting: Parallel Compare Exchange Operation ❖ A parallel compare-exchange operation. Processes Pi and Pj send their elements to each other. Process Pi keeps min{ai, aj}, and Pj keeps max{ai, aj}.
- 6. Sorting: Parallel Compare Split Operation ❖ A compare-split operation. Each process sends its block of size n/p to the other process. ❖ Each process merges the received block with its own block and retains only the appropriate half of the merged block. ❖ In the example, process Pi retains the smaller elements and process Pj retains the larger elements.
- 7. Sorting: Parallel Compare Split Operation
- 8. Bubble Sort and its Variants ❖ The sequential bubble sort algorithm compares and exchanges adjacent elements in the sequence to be sorted. ❖ The complexity of bubble sort is Θ(n2 ). ❖ Bubble sort is difficult to parallelize since the algorithm has no concurrency. ❖ A simple variant, though, uncovers the concurrency.
- 9. Parallelizing Quicksort ❖ Quicksort is one of the most common sorting algorithms for sequential computers because of its simplicity, low overhead, and optimal average complexity. ❖ Quicksort selects one of the entries in the sequence to be the pivot and divides the sequence into two – one with all elements less than the pivot and other greater. ❖ The process is recursively applied to each of the sublists. ❖ In parallel quicksort,choose a pivot from one of the processes and broadcast it to every process.
- 11. Algorithm for Sparse Graph ❖ A graph G = (V, E) is sparse if |E| is much smaller than |V |2 ❖ Examples of Sparse graph: ➢ Linear graph, in which each vertex has two incident edges
- 12. Algorithm for Sparse Graph ❖ Grid graph,in which each vertex has four incident vertices ❖ Random sparse graph.
- 13. Parallel Depth First Search ❖ Depth-first search can be performed in parallel by partitioning the search space into many small, disjunct parts (subtrees) that can be explored concurrently. ❖ Depth-first search algorithm uses idea of backtraching.
- 14. Parallel Breadth First Search