1 / 17

Advanced Algorithms

This lecture provides an introduction to the advanced algorithms course, including information on the instructor, class timings, references, prerequisites, grading, syllabus, and a discussion of the first problem on stable matching.

afranke
Download Presentation

Advanced Algorithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Advanced Algorithms Piyush Kumar (Lecture 1: Introduction) Welcome to COT5405

  2. Today • My Info : Timings for the class • References • Pre-Requisites Survey • How you will be graded • Syllabus • About Advanced Algorithms • Our First Problem • Stable Matching

  3. Instructor Piyush Kumar 161 Love Building Ph: 850-270-1642 Web page: http://piyush.compgeom.com Office Hours: Thursday (after class) 1:45pm to 2:45pm Email: piyush at acm dot org

  4. Class Timings • Timings • Tu, Th • ( 12:30pm – 1:45pm ) • Exams: Look in the course – info sheet.

  5. Other Details • Course web site: • http://piyush.compgeom.com/teach/AA15/ • Textbook.

  6. References • Klienberg / Tardos • Algorithm Design • Other References • [CLRS] T. Cormen, C. Leiserson, R. Rivest, and C. Stein.Introduction to Algorithms (2nd edition). • [MR] R. Motwani and P. Raghavan.Randomized Algorithms. CUP, 1995. • [V] V. V. Vazirani.Approximation Algorithms. • [AMO]. Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993. • My slides and notes

  7. PreReq • Algorithms (COP 4531 or higher) • C++ • Basic Math skills • Lots of Time… • ToDo List: • Get a LinProg Account Today! • Your first home work is due next week • Get a copy of the text book.

  8. PreReq • COP 4531 or higher (What this class does not cover) • Basic Asymptotic analysis / Recursions • Simple Data Structures (PQs, BBTs, …) • Preliminary Graph Algorithms: DFS/BFS/MSTs • Easy Divide and Conquer: Mergesort/Quicksort/…

  9. Grading* • Homework : 20% • Class Participation : 10% • Two Surprise quizzes : 20% • Class Project: 10% • Midterm : 15% • Final Exam : 25%

  10. Syllabus* • Network Flows • Advanced Data Structures • Compression • Optimization • Approximation Algorithms • Online Algorithms • Parallel / External memory / Cache oblivious algorithms • Introduction to Computational geometry • Algorithms from machine learning • Popular Demand Topics - ? * Tentative

  11. Illustrative problems

  12. b e h Interval Scheduling jobs don't overlap • Input. Set of jobs with start times and finish times. • Goal. Find maximum cardinality subset of mutually compatible jobs. a b c d e f g h Time 0 1 2 3 4 5 6 7 8 9 10 11

  13. Weighted Interval Scheduling • Input. Set of jobs with start times, finish times, and weights. • Goal. Find maximum weight subset of mutually compatible jobs. 23 12 20 26 13 20 11 16 Time 0 1 2 3 4 5 6 7 8 9 10 11

  14. Bipartite Matching • Input. Bipartite graph. • Goal. Find maximumcardinality matching. A 1 B 2 C 3 D 4 E 5

  15. 1 4 5 6 Independent Set subset of nodes such that no two joined by an edge • Input. Graph. • Goal. Find maximum cardinality independent set. 2 1 4 5 3 7 6

  16. Competitive Facility Location • Input. Graph with weight on each each node. • Game. Two competing players alternate in selecting nodes. Not allowed to select a node if any of its neighbors have been selected. • Goal. Select a maximum weight subset of nodes. 10 1 5 1 15 1 5 15 5 10 Second player can guarantee 20, but not 25.

  17. Five Representative Problems • Variations on a theme: independent set. • Interval scheduling: n log n greedy algorithm. • Weighted interval scheduling: n log n dynamic programming algorithm. • Bipartite matching: nk max-flow based algorithm. • Independent set: NP-complete. • Competitive facility location: PSPACE-complete.

More Related