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Design & Analysis of Algorithms

An algorithm is a sequence of steps to solve the problem of the design and analysis. It is very important to design the algorithm and solve the problems of the different types of the branch including computer science and the information technology. It introduces the concepts of designing Strategies, Complexity analysis of Algorithms and the methods including in the algorithms. It is a finite set of the specific problem or a different class problem called algorithms.

It includes- Input Output Definiteness Effectiveness

Design of algorithm-

• Implements
• Experiments
• Design
• Analyze

Analysis of algorithms-

- Issues

• correctness
• time efficiency
• space efficiency
• optimiality

- Approaches

• theoretical analysis
• empirical analysis

Design & Analysis of Algorithms

• Simple algorithms ,computer algorithms, analysis of sophisticated algorithms.
• Designing Strategies, Complexity analysis of Algorithms,  problems on Graph Theory and Sorting methods.
• Top down design, Heaps, Data structures, Queues, Priority queues, Trees, Strategies of algorithm design, divide and conquer, Asymptotic costs.
• Distributed Systems Algorithms, Matrix algorithm, Hash tables, Discrete optimization algorithms, Depth first search, Simple recurrence elation, Breadth first search, Matrix algorithm
• Parallel algorithms,General Combinatorial Algorithms, Encryption techniques, Scheduling theory, Network Theory,Graph Algorithms,Network Flows, Graph Drawing, Routing for Graphs, Sequence Sorting

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Related topics for Assignment help

• Algorithm analysis: asymptotic notation, probabilistic analysis,Data Structure: hash table, binary search tree, red-black tree,Sorting: heap sort, quick sort, sorting in linear time,Algorithm design: divide and conquer, greedy algorithms, dynamic programming
• Graph algorithms: breadth-first search, depth-first search, minimum spanning trees, single-source,shortest paths, all-pair shortest paths,NP-completeness: Vertex-cover problem; Traveling-salesman problem, set-cover problem.
• Elementary data structure, Hash Tables, Binary Tree, Red-Black Tree,Time Complexity, Space Complexity, Asymptotical Notation,Sorting Insertion sort, Bubble sort, Heapsort, Quicksort, Linear time sorting
• Divide and conquer, Greedy algorithms, Dynamic programming,Graph ,algorithms,Breadth-first search, Depth-first search, Minimum spanning trees, Single-Source Shortest Paths,All-Pair Shortest paths,NP Completeness,Introduction, Approximation Algorithms,Vertex-cover problem; Traveling-salesman problem, set-cover problem,Asymptotic Analysis and Growth of Functions; Trees, Heaps, and Graphs; and Recurrences.
• Greedy Algorithms: Minimum spanning tree, Union-Find algorithms, Kruskal's Algorithm,Clustering, Huffman Codes, and Multiphase greedy algorithms.
• Dynamic Programming: Shortest paths, negative cycles, matrix chain multiplications, sequence alignment, RNA secondary structure, application examples.
• Network Flow: Maximum flow problem, Ford-Fulkerson algorithm, augmenting paths, Bipartite matching problem, disjoint paths and application problems.
• NP and Computational tractability: Polynomial time reductions; The Satisfiability problem; NPComplete problems; and Extending limits of tractability.Approximation Algorithms, Local Search and Randomized Algorithms
• Applications of Algorithms,Randomized data structures,Greedy algorithms,Graph algorithms,Minimum spanning trees,Network ﬂow,Phylogenetic trees,Optimization,
• stable matchings and disjoint sets and union ﬁnd knapsack problems and multiple sequence alignment,Byzantine agreement and fair division algorithms
• primality tests and Sudoku and latin square solvers,approximation algorithms and linear regression ,link prediction in social networks and PageRank algorithm

Design & Analysis of Algorithms

• Ford-Fulkerson max-ﬂow algorithm (graphs),Back-tracking Sudoku solver (search),Bron-Kerbosch max-clique algorithm (search),Fortune’s algorithm for Voronoi diagrams (computational geometry)
• Christoﬁdes’ algorithm for Traveling Salesman Problem (approximation),AVL tree (data structures),Fibonacci heap (data structures),Algorithm
• randomized input generator
• efficient algorithms,recursion,divide and conquer,balancing,dynamic programming,greedy method,network flow,linear programming,Correctness,analysis of algorithms,NP-completeness
• algebraic algorithms,combinational algorithms,techniques for proving lower bounds on complexity,algorithms for special
Design and analysis of algorithims:
• Analysis of algorithms,Insertion sort, Merge-sort, Growth of functions,Asymptotic analysis,,Recurrences,Divide-and-conquer, Heapsort, Quicksort, Medians and order statistics, Hashing.
• Hash functions,Hash tables,Binary search trees,Red-black trees,2-3 trees,,B-trees,Dynamic,Programming,Greedy algorithms,Amortized algorithms,Maximum flow,Elementary graph,Algorithms
• Minimum spanning trees,Single-source shortest paths,All-pairs shortest paths,Np-completeness,String matching,Reference,Algorithm analysis
• Asymptotic notation,Probabilistic analysis,Data structure,Hash table,Binary search tree,Red-black tree,Sorting: heap sort,Quick sort,Sorting in linear time,Algorithm design,Divide and conquer
• Greedy algorithms,Dynamic programming,Graph algorithms,Breadth-first search,Depth-first search,Minimum spanning trees,Single-source,Shortest paths,All-pair shortest paths,Np-completeness
• Vertex-cover problem,Traveling-salesman problem,Set-cover problem,Algorithm implementation topics,Introduction,Some representative problems,Complex data structures,Graph algorithms
• Greedy algorithms,Divide and conquer,Dynamic programming,Network flow,Np completeness,Approximation algorithms
• Problem, algorithm definitions,Decidability, Halting Problem,Tractability, Towers of Hanoi,Algorithm Complexity, lower and upper bounds,NP completeness, Coping with Intractability,
• Fundamentals,Orders of Magnitude,Growth rates, some common bounds,Polynomial Evaluation,Arithmetic and geometric series,,harmonic numbers, sets, relations, functions, combinations,
• Lower bounds,Example problems and their lower bounds,Comparison problems,Tournaments, ,Recurrence Relations,Substitution, repeated substitution,Master Method, examples of use,Linear homogeneous Recurrence relations
• Fibonacci,Linear Inhomogeneous Recurrence relations, ,Sorting and Priority Queues,Heapsort, analysis,Priority Queues, insert, extract, increase key,Quicksort, worst and average case complexity,
• Graph Traversals,Graph representations,Breadth first traversal, discovery times, breadth first tree,Depth First Search, time stamps, nesting, depth first tree, white path theorem
• Topological Sort, Strongly Connected Components, ,Greedy Algorithms,Recursive Approach and Proof Technique,Activity Selection,Minimal Spanning Trees,Huffman Codes
• Dynamic Programming:Optimization Problems, Scheduling example,Optimal Substructure,Longest Common Subsequence, BackTrack: Search Problems, examples n-Queens and Subset sum
• Iterative and Recursive Back Track Schemata, Shortest Paths Problems:Problem Categories, negative weights and Cycles, Convergence and Bound Properties,Single Source Shortest Paths, Bellman-Ford
• SSSP in DAGs, Dijkstra,All pairs Shortest Paths, Floyd-Warshall, Predecessors in Floyd-Warshall,Transitive Closure
• Asymptotic Notation, Sums, Logs,Three Great Algorithmic Paradigms,,Recursion, Proofs, Induction, Recurrences, Divide and Conquer,Searching Graphs: Depth First, Breadth First, Best First
• Topological Sort, Strongly Connected Components,NP-Completeness,Dynamic Programming,Greedy Algorithms, Minimum Spanning Trees, Shortest Paths,Priority Queue ADT, Amortized Analysis
• Pairing Heaps,Disjoint sets, Union-Find ADT,Transitive Closure,All Pairs Shortest Paths,,Traveling Salesperson Problem,Maximum Network Flow:,ultimate greedy algorithm,Algorithm Analysis,Mathematical Induction,Summation Techniques,Recurrence Relations,Design & Analysis of Algorithms:,Divide and conquer,Greedy Algorithm
• Dynamic Programming,Backtracking,Branch-Bound Research report,Lower Bound Theory,Sorting and Searching,NP-Complete Problems: Basic Concepts,,NP-Hard & NP-Complete Problem
• Design and analysis of algorithms, asymptotic notation, recurrences, randomized algorithms, sorting and selection, balanced binary search trees, augmented data structures, advanced data structures
• algorithms on strings, graph algorithms,geometric algorithms, greedy algorithms, dynamic programming and NP completeness.
Design and Analysis of Algorithms:
• Basic techniques :Sorting,searching,graph algorithms,computational geometry,string processing ,NP completeness,Design techniques ,dynamic programming ,greedy method,Asymptotic,worst case,average case ,amortized analyses,
• Data structures including heaps,hash tables,binary search trees ,red black trees,Worst and average case analysis. ,Recurrences and asymptotics. ,Efficient algorithms for sorting, searching, and selection. ,Data structures: binary search trees,
• heaps, hash tables. ,Algorithm design techniques: divide-and-conquer, dynamic programming, greedy algorithms, amortized analysis, randomization. ,Algorithms for fundamental graph problems: minimum-cost spanning tree, connected components, topological sort, and shortest paths. ,Possible additional topics: network flow, string searching
• Interval Scheduling Assignment 1 Out:Divide & Conquer: Convex Hull, Median Finding ,Smarter Interval Scheduling, Master Theorem, Strassen's Algorithm,FFT ,Van Emde Boas Trees ,B-trees , Amortization: Union-find ,Amortized Analysis
• Randomization: Matrix Multiply, Quicksort,Randomized Median , Skip Lists ,Universal & Perfect Hashing ,Augmentation: Range Trees ,Dynamic Programming: Advanced DP ,All-pairs Shortest Paths ,Greedy Algorithms: Minimum Spanning Tree
• Incremental Improvement: Max Flow, Min Cut ,Matching ,Applications of Network Flow & Matching ,Linear Programming: LP, Reductions, Simplex ,Complexity: P, NP, NP-completeness, Reductions ,Complexity: More Reductions
• Approximation Algorithms,Fixed-parameter Algorithms , Synchronous Distributed Algorithms: Symmetry-breaking. Shortest-paths Spanning Trees ,Asynchronous Distributed Algorithms: Shortest-paths Spanning Trees
• Distributed Algorithms ,Cryptography: Hash Functions ,Encryption  ,Cache-oblivious Algorithms: Medians & Matrices ,Searching & SortingMedian finding, solving recurrences,Median finding, interval scheduling
• Greedy algorithms, minimum spanning trees: Kruskal's ,Minimum spanning trees: Prim's ,Fast Fourier transform ,Dynamic programming, all pairs shortest paths: Floyd-Warshall ,All-pairs shortest paths II: Johnson's
• Randomized algorithms, high probability bounds ,Hashing ,Amortized analysis 17 ,Competitive analysis , Network flows ,Preparation for take-home exam ,van Emde Boas data structure ,Advanced data structures: disjoint sets
• P vs. NP ,Approximation algorithms ,Compression ,Sub-linear time algorithms , Clustering ,Derandomization ,Computational geometry.Recurrence relations,master theorem,amortized analysis,linear-time selection,
• Algorithms and computational complexity,Asymptotic notation,Pseudocode,Algorithm design techniques,Divide-and-Conquer(Quicksort),Dynamic programming(matrix chain multiplication),Greedy algorithms(Huffman codes),
• Topological sorting,Algebraic algorithms,Strassen matrix multiplication algorithm,The Four Russians boolean matrix multiplication,Winograd's algorithm,LUP decomposition of matrices,Applications of LUP decomposition,
• Heapsort and Heaps,Binomial Heaps,Fibonacci Heaps,Minimum Spanning Trees,
• Balanced Binary Search Trees such as Splay Trees,Union-Find Data Structure,Algorithmic Techniques,Greedy Algorithms and Matroids,Shortest Paths and Dynamic Programming,Divide and Conquer,Randomized algorithms such as Treaps,Graph algorithms,Network Flows and Bipartite Matching

Few Topics are:

• correctness and analysis of time and space requirements
• lower bounds
• sorting and medians
• amortized analysis of advanced data structures
• graph algorithms
• strongly connected components,
• shortest pathsminimum spanning trees
• maximum flows and bipartite matching
• NP-Completeness

Algorithms