CS 4234 Optimization Algorithms Welcome CS 4234 Overview

CS 4234 Optimization Algorithms Welcome!

CS 4234 Overview q Optimization Algorithms http: //www. comp. nus. edu. sg/~gilbert/CS 4234 q Instructor: Seth Gilbert Office: COM 2 -323 Office hours: by appointment

Optimization Algorithms Optimization: Find the minimum/maximum…

Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items

Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items Combinatorial: a collection of items generated by counting, combining, and enumerating.

Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items Combinatorial: a collection of items generated by counting, combining, and enumerating. Examples: Graphs Matroids Similar structures…

Combinatorial Optimization Find the “best” item in a large set of items: Problem Set of items Size Difficulty Searching List of integers Linear Easy Shortest paths All paths in a graph Exponential Easy Minimum spanning tree All spanning trees Exponential Easy Steiner tree All steiner trees Exponential Hard Travelling salesman All possible tours Exponential Hard Matching All possible matchings Exponential Easy Bipartite vertex cover All possible covers Exponential Easy Vertex cover All possible covers Exponential Hard Maximum clique All possible subsets Exponential Very Hard

Combinatorial Optimization Find the “best” item in a large set of items: Problem Difficulty Maintain student records Easy Data compression Easy Program halting problem VLSI chip layout Impossible Hard Exam timetable scheduling Hard Job assignment problem Easy Computer deadlock problem Easy Finding patterns in a database Easy

Combinatorial Optimization Operations Research: How to make better decisions (e. g. , maximize profit) Project planning / critical path analysis Facility location: where to open stores / plants Floorplanning: layout of factory or computer chips Supply chain management Berth assignment problem (BAP): port management Assignment problems (e. g. , weapon target assignment) Routing / transportation problems: buses, subways, trucking. Airline ticket pricing

Optimization Algorithms Optimization: Find the minimum/maximum: Discrete: a collection of items Combinatorial: a collection of items generated by counting, combining, and enumerating. Continuous: given a function f(x), find the vector x that maximizes f(x).

Optimization Algorithms

“If you need your software to run twice as fast, hire better programmers. But if you need your software to run more than twice as fast, use a better algorithm. ” -- Software Lead at Microsoft

“. . . pleasure has probably been the main goal along. But I hesitate to admit it, because computer scientists want to maintain their image as hardworking individuals who deserve high salaries. . . ” -- D. E. Knuth

“. . . pleasure has probably been the main goal along. But I hesitate to admit it, because computer scientists want to maintain their image as hardworking individuals who deserve high salaries. . . ” -- D. E. Knuth

CS 4234 : Optimization Algorithms Brand new class: – We can make this class what we want. – Talk to me about your goals, interests, etc.

CS 4234 : Optimization Algorithms Brand new class: – We can make this class what we want. – Talk to me about your goals, interests, etc. Where did this class come from? – CS 5234: Combinatorial and Graph Algorithms – More general: all sorts of optimization (not only graphs). – More specific: just optimization

Optimization Algorithms Target students: – Advanced (3 rd or 4 th year) undergraduates – Interested in algorithms – Interested in tools for solving hard problems Prerequisites: – CS 3230 (Analysis of Algorithms) – Mathematical fundamentals

CS 4234 Overview q Mid-term exam October 6 In class q Final exam November 25 Exams will be graded and returned.

CS 4234 Overview q Grading 40% Problem sets 25% Mid-term exam 35% Final exam q Problem sets – 5 -6 sets (about every 1 -2 weeks) – Focused on algorithm design and analysis.

CS 4234 Overview q Mini-Project Small project Idea: put together some of the different ideas we have used in the class. Time scale: last 2 -3 weeks of the semester.

CS 4234 Overview q Released today/tomorrow Survey: On IVLE. What is your background? Not more than 10 minutes. PS 1: Released tomorrow.

CS 4234 Overview q Problem set grading Simple scheme: 3 : excellent, perfect answer 2 : satisfactory, mostly right 1 : many mistakes / poorly written 0 : mostly wrong / not handed in -1 : utter nonsense

CS 4234 Overview q What to submit: Concise and precise answers: Solutions should be rigorous, containing all necessary detail, but no more. Algorithm descriptions consist of: 1. Summary of results/claims. 2. Description of algorithm in English. 3. Pseudocode, if helpful. 4. Worked example of algorithm. 5. Diagram / picture. 6. Proof of correctness and performance analysis.

CS 4234 Overview q How to draw pictures? By hand: Either submit hardcopy, or scan, or take a picture with your phone! Or use a tablet / i. Pad… Digitally: 1. 2. 3. 4. xfig (ugh) Omni. Graffle (mac) Powerpoint (hmmm) ? ? ?

CS 4234 Overview q Policy on plagiarism: Do your work yourself: Your submission should be unique, unlike anything else submitted, on the web, etc. Discuss with other students: 1. Discuss general approach and techniques. 2. Do not take notes. 3. Spend 30 minutes on facebook (or equiv. ). 4. Write up solution on your own. 5. List all collaborators. Do not search for solutions on the web: Use web to learn techniques and to review material from class.

CS 4234 Overview q Policy on plagiarism: Penalized severely: First offense: minimum of one letter grade lost on final grade for class (or referral to So. C disciplinary committee). Second offense: F for the class and/or referral to So. C. Do not copy/compare solutions!

Textbooks Introduction to Algorithms – Cormen, Leiserson, Rivest, Stein – Recommended…

Textbooks Algorithm Design – Kleinberg and Tardos – Recommended…

CS 4234 Overview q Topics (tentative, TBD) Introduction to combinatorial optimization Vertex cover, set cover, Steiner tree, TSP Flows and matching Maximum flow, bipartite matching Linear programming LPs, duality, relaxations, rounding Continuous optimization Gradient descent, meta-heuristics