Logistics management class lectures_19227488-Algorithm-Lectures

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Lecture Notes for Algorithm Analysis and DesignSandeep Sen1March 16, 20081 Departmentof Computer Science and Engineering, IIT Delhi, New Delhi 110016, India.E-mail:ssen@cse.iitd.ernet.inContents1 Model and Analysis1.1 Computing Fibonacci numbers .1.2 Fast Multiplication . . . . . . .1.3 Model of Computation . . . . .1.4 Other models . . . . . . . . . .1.4.1 External memory model1.4.2 Parallel Model . . . . . .............2 Warm up problems2.1 Euclids algorithm for GCD . . . .2.1.1 Extended Euclids algorithm2.2 Finding the k-th element . . . . . .2.2.1 Choosing a random splitter2.2.2 Median of medians . . . . .2.3 Sorting words . . . . . . . . . . . .2.4 Mergeable heaps . . . . . . . . . .2.4.1 Merging Binomial Heaps . .....................................................................................3 Optimization I :Brute force and Greedy strategy3.1 Heuristic search approaches . . . . . . . . . .3.1.1 Game Trees * . . . . . . . . . . . . . .3.2 A framework for Greedy Algorithms . . . . . .3.2.1 Maximal Spanning Tree . . . . . . . .3.2.2 A Scheduling Problem . . . . . . . . .3.3 Efficient data structures for MST algorithms .3.3.1 A simple data structure for union-find3.3.2 A faster scheme . . . . . . . . . . . . .3.3.3 The slowest growing function ? . . . .3.3.4 Putting things together . . . . . . . . .1..........

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