
This a graduate course on algorithms and data structures. Topics that we plan to cover include: basic programming paradigms (recursion, divide and conquer, greedy, dynamic programming), data structures (unionfind, heaps), graph algorithms (shortest paths, spanning trees, network flows, matching, mincut), randomized algorithms, linear programming and duality, semidefinite programming, approximation algorithms, online algorithms. Topics may be added / removed, depending on interest and time available. 

We will assume knowledge of the basics of algorithms and analysis and data structures, including basic sorting and searching algorithms, graph traversal, solving recurrences, bigoh notation, and NPcompleteness. These prerequisites may be obtained from the CLRS reference book. 

Classes will be held Tuesday and Thursday 9:30  11 am in A201.
Evaluation will be on the basis of assigments (50%), a midterm (25%), and a final exam (25%). The weightage of these may be slightly modified later. Office hours are Wednesdays 9:30  11 am. 

The topics we cover will mostly be from the book Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein, for the first part of the course. However, our treatment and notation will differ. Other good reference materials are
Our treatment will often differ from that in books, and I may cover topics out of order. I will post an outline of topics covered in each lecture below, including source material.



Logistics. An O(n log n) algorithm for finding the closest pair of points in the plane. An O(n) algorithm for finding the median of a set of numbers (incomplete).
Other references: Sections 33.4 and 9.3 from CLRS.  
Completing medianfinding in O(n) time. Polynomial multiplication via the DFT in O(n log n) time.
Other references: Chapter 30 from CLRS, excluding Section 30.3.  
Dynamic programming: Longest increasing subsequence, and optimal BSTs. Note that the algorithm we actually did in class is different from the algorithm in the notes. In class, we had a onedimensional table for the DP, where each entry stored the length of the LIS that ended in that entry.
Other references: Chapter 3 from Jeff Erickson's book, available here (particularly Sections 3.6 and 3.9).  
A faster algorithm for Longest Increasing Subsequence. Greedy algorithms  matchings.  
Greedy algorithms: Huffman coding. Matroids and greedy algorithms.
Other references: CLRS Chapter 17.  
Continued with matroids from previous class. Greedy job selection with penalties. Started discussing Dijkstra's algorithm.
Other references: CLRS Chapter 17, and CLRS Section 24.3 for Dijkstra's algorithm.  
Dijkstra's algorithm: with minheaps, and with Fibonacci heaps.
Other references: CLRS Section 24.3 for Dijkstra's algorithm, Chapter 6 for min heaps, and Chapter 19 for Fibonacci heaps.  
Kruskal's algorithm for MSTs, and the unionfind data structure: here.
Other references: Sariel HarPeled's notes, available here. 





