Qualifying Exam Syllabus for COMPSCI 532: Algorithms

Exam is Closed Book

Qualifying Exam Syllabus for COMPSCI 532

  • Design Techniques: Divide-and-conquer, recurrence relations, greedy algorithms, dynamic programming, randomization.
  • Sorting and searching: various sorting algorithms, worst case and average case analysis, linear time selection.
  • Data structures: Heaps, binary search trees, height balanced trees, amortization, union-find, hashing.
  • Graph algorithms: graph traversal, biconnectivity, strongly connected components, topological sorting, minimum spanning trees, shortest paths, max flow, min cut.
    • Geometric algorithms: closest pair, convex hull
    • Algebraic algorithms: polynomial multiplication, FFT
  • Intractability: Easy and hard problems, NP-Completeness, reducibility, approximation algorithms.

References:

  • T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Introduction to Algorithms, MIT Press. (Chapters 1-13, 15-17, 21-26, 34-35).
  • S. Dasgupta, C. Papadimitriou, U. Vazirani, Algorithms, McGraw-Hill.
  • J. Kleinberg and E. Tardos, Algorithm Design, Addison Wesley (Chapters 1-8, 11.1-11.4).

Sample Exams:

 

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