2 Today My Info : Timings for the class References Pre-Requisites Survey How you will be gradedSyllabusAbout Advanced AlgorithmsOur First ProblemStable Matching
3 InstructorPiyush Kumar 161 Love Building Ph: Web page: Office Hours: Tuesday (after class) 4:50 to 5:50 piyush at acm dot org
4 Class Timings Timings Exams: Look in the course – info sheet. Tuesday , Thursday( 3:35pm – 4:50pm )First Class: 25th AugExams: Look in the course – info sheet.
5 Other Details Textbook. Course web site: Textbook.
6 References Klienberg / Tardos Other References Algorithm Design [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 AccountGet a copy of the text book.
8 PreReq COP 4531 or higher (What this class does not cover) Basic Asymptotic analysis / RecursionsSimple Data Structures (PQs, BBTs, …)Preliminary Graph Algorithms: DFS/BFS/MSTsEasy Divide and Conquer: Mergesort/Quicksort/…
12 Interval Schedulingjobs don't overlapInput. Set of jobs with start times and finish times.Goal. Find maximum cardinality subset of mutually compatible jobs.abhebcActivity selection = interval schedulingOPT = B, E, HNote: smallest job (C) is not in any optimal solution, job that starts first (A) is not in any optimal solution.defghTime1234567891011
13 Weighted Interval Scheduling Input. Set of jobs with start times, finish times, and weights.Goal. Find maximum weight subset of mutually compatible jobs.2312202613201116Time1234567891011
15 Independent Set Input. Graph. subset of nodes such that no two joined by an edgeInput. Graph.Goal. Find maximum cardinality independent set.65141245367
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.10151551511510subset of selected nodes must form an independent setSecond 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.