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.

AMS 210 or Mat 211; CSE 214 or CSE 260

• Ability to perform worst-case asymptotic algorithm analysis
• Ability to define and use classical combinatorial algorithms for problems such as sorting, shortest paths and minimum spanning trees
• Knowledge of computational intractability and NP completeness

• Steven Skiena, The Algorithm Design Manual, second edition, Springer-Verlag, 2008.

• 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 is a theory course.