The course is an introduction to the design and analysis of efficient algorithms, with emphasis on developing techniques for the design and rigorous analysis of algorithms rather than on implementation. Algorithmic problems include sorting and searching, discrete optimization, and algorithmic graph theory. Design techniques include divide-and-conquer methods, dynamic programming, greedy methods, graph search, as well as the design of efficient data structures. Methods of algorithm analysis include asymptotic notation, evaluation of recurrences, and the concepts of polynomial-time algorithms. NP-completeness is discussed at the end the course. Students who complete the course will have demonstrated the ability to use divide-and-conquer methods, dynamic programming methods, and greedy methods, when an algorithmic design problem calls for such a method. They will have learned the design strategies employed by the major sorting algorithms and the major graph algorithms, and will have demonstrated the ability to use these design strategies or modify such algorithms to solve algorithm problems when appropriate. They will have derived and solved recurrences describing the performance of divide-and-conquer algorithms, have analyzed the time and space complexity of dynamic programming algorithms, and have analyzed the efficiency of the major graph algorithms, using asymptotic analysis.
Topics covered include: sorting and searching; divide-and-conquer; dynamic programming; graph search; shortest paths; minimum spanning trees; network flow; hashing and binary search trees, as time permits. NP-complete problems are discussed at the end of the course.