Mathematical analysis of a variety of computer algorithms including searching, sorting, matrix multiplication, fast Fourier transform, and graph algorithms. Time and space complexity. Upper-bound, lower- bound, and average-case analysis. Introduction to NP completeness. Some machine computation is required for the implementation and comparison of algorithms.

This course is offered as CSE 373 and MAT 373.

MAT 211 or AMS 210; CSE 214

• Provide a rigorous introduction to worst-case asymptotic algorithm analysis.
• Develop classical graph and combinatorial algorithms for such problems as sorting, shortest paths and minimum spanning trees.
• Introduce the concept of computational intractability and NP completeness.

• Fundamentals of Algorithmic, Gilles Brassard and Paul Bratley, Prentice Hall ISBN: 0-13-335068-1
• The Algorithm Design Manual, Steven Skiena, Springer-Verlag, NY 1997

• Preliminaries: Algorithm correctness, asymptotic (big-Oh) notation, problem modeling , (1.5 weeks)
• Data Structures: Review of elementary data structures (stacks/queues), dictionary data structures such as binary search trees, priority queues such as heaps, (1.5 weeks)
• Sorting: Algorithmic applications of sorting, analysis of quicksort, mergesort, and heapsort, distribution/radix sorting, lower bounds, (1.5 weeks)
• Problem Decomposition Algorithms: Dynamic programming (edit distance, chain matrix multiplication), divide-and-conquer algorithms (binary search and variants), (1.5 weeks)
• Combinatorial Search: Backtracking, exhaustive search, permutations/subsets, (1 week)
• Graph Algorithms: graph data structures (adjacency lists/arrays), BFS/DFS, topological sorting, connectivity testing, minimum spanning trees, shortest paths (Dijkstra's and Floyd's algorithms), (3 weeks)
• Intractability: problem reductions, NP-completeness, approximation algorithms, (2 weeks)

Not applicable since it’s a theory course.