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**Piyush Kumar (Lecture 1: Introduction)**

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

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**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

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Instructor Piyush Kumar 161 Love Building Ph: Web page: Office Hours: Tuesday (after class) 4:50 to 5:50 piyush at acm dot org

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**Class Timings Timings Exams: Look in the course – info sheet.**

Tuesday , Thursday ( 3:35pm – 4:50pm ) First Class: 25th Aug Exams: Look in the course – info sheet.

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**Other Details Textbook. Course web site:**

Textbook.

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**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

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**PreReq Algorithms (COP 4531 or higher) C++ Basic Math skills**

Lots of Time… ToDo List: Get a LinProg Account Get a copy of the text book.

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**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/…

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**Grading* Homework : 25% Class Participation : 5%**

Two Surprise quizzes : 10% Class Project: 20% Midterm : 15% Final Exam : 25%

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**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

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**Illustrative problems**

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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 h e b c Activity selection = interval scheduling OPT = B, E, H Note: smallest job (C) is not in any optimal solution, job that starts first (A) is not in any optimal solution. d e f g h Time 1 2 3 4 5 6 7 8 9 10 11

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**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 1 2 3 4 5 6 7 8 9 10 11

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**Bipartite Matching Input. Bipartite graph.**

Goal. Find maximum cardinality matching. A 1 B 2 C 3 D 4 E 5

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**Independent Set Input. Graph.**

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

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**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 15 5 1 5 1 15 10 subset of selected nodes must form an independent set Second player can guarantee 20, but not 25.

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**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.

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