PPT-1 Spanning Trees, greedy algorithms

Lecture 22 CS2110 Fall 2017 1 We demo A8 Your space ship is on earth and you hear a distress signal from a distance Planet X Your job Rescue stage Fly your ship to Planet X as fast as you can. - S. Kapoor and H. Ramesh. Speakers: . 李孟韓. 1. , . 林蔚茵. 2. , . 莊秋芸. 3. , . 黃稚穎. 4. Reference. H. N. Gabow and E. W. Myers: Finding all spanning trees of directed and undirected graphs, . Optimization problems, Greedy Algorithms, Optimal Substructure and Greedy choice. Learning & Development Team. http://academy.telerik.com. . Telerik Software Academy. Table of Contents. Optimization Problems. Yuli. Ye . Joint work with Allan Borodin, University of Toronto. Why do we study greedy algorithms? . don’t. A quote from Jeff Erickson’s algorithms book. . Everyone should tattoo the following sentence on the back of their hands, right under all the rules about logarithms and big-Oh notation. to . Greedy Routing Algorithms . in Ad-Hoc Networks. ○. Truong . Minh . Tien. Joint work with. Jinhee. . Chun, . Akiyoshi. . Shioura. , . and Takeshi . Tokuyama. Tohoku University. Japan. Our . Problem. Trees. Spring 2014. Sukumar Ghosh. What is a tree?. Rooted tree: recursive definition. Rooted tree terminology. Rooted tree terminology. A . subtree. Rooted tree terminology. Important properties of trees. The two key components. Optimal Sub-structure. You solve the problem by solving a sub-problem optimally. Greedy Property. Using the choice that seems best at the moment leads to the optimal result. This is tougher to show!. : Data Structures & Algorithms. Spanning Trees and Minimum . Spanning Trees. Riley Porter. Winte. r 2017. CSE373: Data Structures & Algorithms. 1. Course Logistics. HW4 due tonight. HW5 out . . Greedy . Algorithms. CSE 680. Prof. Roger Crawfis. Optimization . Problems. For most optimization problems you . want to find, not just . a. solution, but the . best. . solution.. A . greedy algorithm . A . tree. is a connected undirected graph with no simple circuits.. Since a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops.. Therefore, any tree must be a . simple graph. CSE 421 Greedy Algorithms / Interval Scheduling Yin Tat Lee 1 Interval Scheduling Job starts at and finishes at . Two jobs compatible if they don’t overlap. Goal: find maximum subset of mutually compatible jobs. Introduction to Algorithms Greedy Algorithms CSE 680 Prof. Roger Crawfis Optimization Problems For most optimization problems you want to find, not just a solution, but the best solution. A Fall 20151 Week . 7. CSCI-141. Scott C. Johnson. Say we go to the bank to cash our paycheck. We ask the teller for the fewest bills and coins as possible. Moments later the teller gives us our money and we leave. Cormen. . Leiserson. . Rivest&Stein. :. Introduction to Algorithms. Minimal Spanning Trees. Weighted Graphs . G(V, E, w). W: E R. If w=1 for all edges BFS is the solution.. The MST is the way of connecting n vertices at minimal cost of connections.. Minimum spanning tree (MST). Single source shortest path (SSSP), e.g., Dijkstra’s algorithm. We will explore the main properties, with focus on theoretical foundations. MST:. Graph G(V,E): undirected, connected, weighted (arbitrary real weights w() on edges).