Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email.

Slides:



Advertisements
Similar presentations
Single Source Shortest Paths
Advertisements

Lecture 30 CSE 331 Nov 8, HW 7 due today Place Q1, Q2 and Q3 in separate piles I will not accept HWs after 1:15pm DO NOT FORGET TO WRITE DOWN YOUR.
Lecture 38 CSE 331 Dec 7, The last few days Today: Solutions to HW 9 (end of lecture) Wednesday: Graded HW 9 (?), Sample final, Blog post on the.
Lecture 37 CSE 331 Nov 4, Homework stuff (Last!) HW 10 at the end of the lecture Solutions to HW 9 on Monday Graded HW 9 on.
Lecture 28 CSE 331 Nov 9, Flu and HW 6 Graded HW 6 at the END of the lecture If you have the flu, please stay home Contact me BEFORE you miss a.
UMass Lowell Computer Science Analysis of Algorithms Prof. Karen Daniels Spring, 2006 Lecture 2 Monday, 2/6/06 Design Patterns for Optimization.
UMass Lowell Computer Science Analysis of Algorithms Prof. Karen Daniels Fall, 2006 Lecture 2 Monday, 9/13/06 Design Patterns for Optimization Problems.
Lecture 31 CSE 331 Nov 16, Jeff is out of town this week No regular recitation or Jeff’s normal office hours I’ll hold extra Question sessions Mon,
Lecture 16 CSE 331 Oct 9, Announcements Hand in your HW4 Solutions to HW4 next week Remember next week I will not be here so.
Lecture 34 CSE 331 Nov 19, HW 9 due today Q1 in one pile and Q 2+3 in another I will not take any HW after 1:15pm.
Lecture 39 CSE 331 Dec 6, On Friday, Dec 10 hours-a-thon Atri: 2:00-3:30 (Bell 123) Jeff: 4:00-5:00 (Bell 224) Alex: 5:00-6:30 (Bell 242)
Lecture 23 CSE 331 Oct 24, Temp letter grades assigned See the blog post for more details.
Lecture 24 CSE 331 Oct 30, Homework stuff Please turn in your HW 6 Graded HW 5 and HW 7 at the END of the lecture.
Lecture 36 CSE 331 Dec 2, Graded HW 8 END of the lecture.
Lecture 34 CSE 331 Nov 30, Graded HW 8 On Wednesday.
Lecture 32 CSE 331 Nov 15, Feedback Forms Link for the survey on the blog.
Lecture 34 CSE 331 Nov 23, Homework related stuff Graded HW 8+9, solutions to HW 9 the week after Thanksgiving.
Lecture 37 CSE 331 Dec 1, A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) .
Lecture 39 CSE 331 Dec 9, Announcements Please fill in the online feedback form Sample final has been posted Graded HW 9 on Friday.
Lecture 33 CSE 331 Nov 17, Online office hours Alex will host the office hours.
Lecture 25 CSE 331 Nov 2, Adding teeth to group talk Form groups of size at most six (6) Pick a group leader I will ask group leader(s) to come.
Lecture 20 CSE 331 Oct 21, Algorithm for Interval Scheduling R: set of requests Set A to be the empty set While R is not empty Choose i in R with.
Lecture 28 CSE 331 Nov 5, HW 7 due today Q1 in one pile and Q 2+3 in another I will not take any HW after 1:15pm.
Lecture 30 CSE 331 Nov 10, Online Office Hours
CSCI-256 Data Structures & Algorithm Analysis Lecture Note: Some slides by Kevin Wayne. Copyright © 2005 Pearson-Addison Wesley. All rights reserved. 17.
Lecture 38 CSE 331 Dec 2, Review Sessions etc. Atri: (at least ½ of) class next Friday Jiun-Jie: Extra office hour next Friday Jesse: Review Session.
Analysis of Algorithms CS 477/677 Instructor: Monica Nicolescu Lecture 14.
Lecture 23 CSE 331 Oct 24, Reminder 2 points for Piazza participation 3 points for mini-project.
1 Chapter 6-1 Dynamic Programming Slides by Kevin Wayne. Copyright © 2005 Pearson-Addison Wesley. All rights reserved.
Lecture 38 CSE 331 Dec 5, OHs today (only online 9:30-11)
CSE 331: Review.
Lecture 33 CSE 331 Nov 20, HW 8 due today Place Q1, Q2 and Q3 in separate piles I will not accept HWs after 1:15pm Submit your HWs to the side of.
CSE 331: Review August 1, Main Steps in Algorithm Design Problem Statement Algorithm Real world problem Problem Definition Precise mathematical.
Lecture 32 CSE 331 Nov 16, 2016.
Lecture 22 CSE 331 Oct 22, 2010.
Lecture 21 CSE 331 Oct 21, 2016.
Lecture 24 CSE 331 Oct 28, 2016.
Lecture 36 CSE 331 Nov 29, 2017.
Lecture 21 CSE 331 Oct 20, 2017.
Lecture 36 CSE 331 Nov 30, 2016.
Lecture 35 CSE 331 Nov 27, 2017.
Lecture 34 CSE 331 Nov 20, 2017.
Lecture 33 CSE 331 Nov 18, 2016.
Lecture 33 CSE 331 Nov 17, 2017.
Chapter 6 Dynamic Programming
Lecture 35 CSE 331 Nov 28, 2016.
Lecture 37 CSE 331 Dec 1, 2017.
Chapter 6 Dynamic Programming
Lecture 24 CSE 331 Oct 25, 2013.
Lecture 26 CSE 331 Nov 2, 2012.
Richard Anderson Lecture 16a Dynamic Programming
Lecture 37 CSE 331 Nov 30, 2011.
Dynamic Programming Longest Path in a DAG, Yin Tat Lee
Lecture 32 CSE 331 Nov 15, 2017.
Lecture 33 CSE 331 Nov 14, 2014.
Lecture 34 CSE 331 Nov 21, 2016.
Lecture 22 CSE 331 Oct 15, 2014.
Lecture 18 CSE 331 Oct 9, 2017.
Lecture 19 CSE 331 Oct 14, 2011.
Lecture 10 CSE 331 Sep 21, 2012.
Lecture 24 CSE 331 Oct 24, 2014.
Lecture 36 CSE 331 Nov 28, 2011.
Lecture 36 CSE 331 Nov 30, 2012.
Lecture 37 CSE 331 Dec 2, 2016.
Lecture 23 CSE 331 Oct 24, 2011.
Analysis of Algorithms CS 477/677
Lecture 25 CSE 331 Oct 28, 2011.
Lecture 19 CSE 331 Oct 10, 2016.
Lecture 36 CSE 331 Nov 22, 2013.
Lecture 37 CSE 331 Dec 3, 2018.
Presentation transcript:

Lecture 38 CSE 331 Dec 3, 2010

A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) me any objections (or support) by Monday, Dec 6, noon Individual choice for every student

Homework stuff HW 10 posted Graded HW 9 pickups: my office hours today Jeff/Alex next week

Weighted Interval Scheduling Input: n jobs (s i,t i,v i ) Output: A schedule S s.t. no two jobs in S have a conflict Goal: max Σ j in S v j Assume: jobs are sorted by their finish time

Property of OPT OPT(j) = max { v j + OPT( p(j) ), OPT(j-1) }

A recursive algorithm M-Compute-Opt(j) If j = 0 then return 0 M[j] = max { v j + M-Compute-Opt( p(j) ), M-Compute-Opt( j-1 ) } If M[j] is not null then return M[j] return M[j] M-Compute-Opt(j) = OPT(j) Run time = O(# recursive calls)

Bounding # recursions M-Compute-Opt(j) If j = 0 then return 0 M[j] = max { v j + M-Compute-Opt( p(j) ), M-Compute-Opt( j-1 ) } If M[j] is not null then return M[j] return M[j] Whenever a recursive call is made an M value of assigned At most n values of M can be assigned O(n) overall

Property of OPT OPT(j) = max { v j + OPT( p(j) ), OPT(j-1) } Given OPT(1), …, OPT(j-1), one can compute OPT(j) Given OPT(1), …, OPT(j-1), one can compute OPT(j)

Recursion+ memory = Iteration Iteratively compute the OPT(j) values M[0] = 0 M[j] = max { v j + M[p(j)], M[j-1] } For j=1,…,n Iterative-Compute-Opt M[j] = OPT(j) O(n) run time

Reading Assignment Sec 6.1, 6.2 of [KT]

When to use Dynamic Programming There are polynomially many sub-problems Optimal solution can be computed from solutions to sub-problems There is an ordering among sub-problem that allows for iterative solution Richard Bellman

Shortest Path Problem Input: (Directed) Graph G=(V,E) and for every edge e has a cost c e (can be <0) t in V Output: Shortest path from every s to t s t Shortest path has cost negative infinity Assume that G has no negative cycle

Today’s agenda Dynamic Program for shortest path

May the Bellman force be with you