PPT-1 Minimum Cost Flow - Strongly Polynomial Algorithms

Introduction MinimumMean Cycle Canceling Algorithm Repeated Capacity Scaling Algorithm Enhanced Capacity Scaling Algorithm Summary Minimum Cost Flow Problem Strongly Polynomial Algorithms. . NP-Complete. CSE 680. Prof. Roger Crawfis. Polynomial Time. Most (but not all) of the algorithms we have studied so far are easy, in that they can be solved in polynomial time, be it linear, quadratic, cubic, etc.. NETWORK. SIMPLEX . ALGORITHM. A talk by: Lior Teller. 1. A short reminder (it’s been three weeks..). G=(V,E) is a directed graph. Capacity . (. קיבולת. ) function . u. ij. . > 0 for every . Based on the book: Introduction to Management Science. Hillier & Hillier. McGraw-Hill. Minimum Cost Flow. Distribution Unlimited Co. Problem. The Distribution Unlimited Co. has two factories producing a product that needs to be shipped to two warehouses. basic algorithms (Part II). Adi Haviv (+ Ben Klein) 18/03/2013. 1. Lecture Overview. Introduction (Reminder). Optimality Conditions (Reminder). Pseudo-flow. MCF Algorithms: . Successive shortest Path Algorithm. JAMES B. ORLIN. Aviv Eisenschtat . 6/5/2013. Introduction. Developed in 1989. Based . on the Edmonds & Karp scaling algorithm. Fastest strongly polynomial algorithm for min-cost flow. Fairly simple and intuitive . Ben Klein – . 11/03/13. Introduction. Applications. Optimality Conditions. Primal Dual in LP. Algorithms. Introduction. Applications. Optimality Conditions. Primal Dual in LP. Algorithms. Max flow – A reminder. Overview. . Recap:. Min Cost Flow, Residual Network. Potential and Reduced Cost. Polynomial Algorithms. Approach. Capacity Scaling. Successive . Shortest . Path Algorithm Recap. Incorporating Scaling. (a brief introduction to theoretical computer science). slides by Vincent Conitzer. Set Cover . (a . computational problem. ). We are given:. A finite set S = {1, …, n}. A collection of subsets of S: S. Network Optimization Models. 10.1 Prototype Example. The road system for Seervada Park. Location . O. : park entrance. Location . T. : a scenic wonder. Trams transport sightseers from park entrance to location . Cost . Flow, Kevin D. Wayne. Eyal Dushkin – 03.06.13. Reminder – Generalized Flows. We are given a graph . We associate a positive . with every . arc. Assume that if 1 unit of flow was sent from node . Polynomial Function. Definition: A polynomial function of degree . n. in the variable x is a function defined by. Where each . a. i. (0 ≤ . i. ≤ n-1) is a real number, a. n. ≠ 0, and n is a whole number. . Richard Anderson. Winter 2013. Lecture 4. Announcements. Reading. For today, sections 4.5, 4.7, . 4.8, 5.1, 5.2. Interval Scheduling. Highlights from last lecture. Greedy Algorithms. Dijkstra’s. Algorithm. Optical flow , A tutorial of the paper: KH Wong Optical Flow v.5a (beta) 1 G. Farneback , “Two-frame Motion Estimation based on Polynomial Expansion”, 13th Scandinavian Conference, SCIA 2003 Halmstad Matching Algorithms and Networks Algorithms and Networks: Matching 2 This lecture Matching: problem statement and applications Bipartite matching (recap) Matching in arbitrary undirected graphs: Edmonds algorithm