PPT-Min Cost Flow: Polynomial Algorithms

Overview Recap Min Cost Flow Residual Network Potential and Reduced Cost Polynomial Algorithms Approach Capacity Scaling Successive Shortest Path Algorithm Recap Incorporating Scaling. 2 02 02 02 Flash point TOC F T 79 100 150 150 150 Distillation test T 78 Distillate percentage by volume of tota l distillate to 680F to 437F 25 10 to 500F 40 70 15 55 35 15 to 600F 75 93 60 87 45 80 15 75 Residue from distillation volume . 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.. Cue soft triangle Bmin/A min *maj Bmin/A min *maj n7* Bmin/A min n7* Bmin/A min *maj n7F *maj *maj *maj n7Bm Bmin/A min *maj n7* Bmin/A min *maj n7F *maj n7Bm *maj n7Bm *maj n7Bm */A A/* n11Bmin *maj AWA add9 Ain't No Algebra II with . Trigonometry. Ms. Lee. Essential Question. What is a polynomial?. How do we describe its end behavior?. How do we add/subtract polynomials?. Essential Vocabulary. Polynomial . Degree. Dan Castillo. A Brief . H. istory of Knots. (1860’s). Lord Kelvin: . quantum vortices?. Let’s tabulate them just in case. First . table of knots by Peter . Tait. Aye aye!. Mathematical Study of Knots. Introduction. Minimum-Mean Cycle Canceling . Algorithm. Repeated Capacity Scaling . Algorithm. Enhanced Capacity Scaling. Algorithm. Summary. Minimum Cost Flow Problem –. Strongly Polynomial Algorithms. Classify polynomials and write polynomials in standard form. . Evaluate . polynomial expressions. .. Add and subtract polynomials. . Objectives. monomial. degree of a monomial. polynomial. degree of a polynomial. Definitions. Coefficient. : the numerical factor of each term.. Constant. : the term without a variable.. Term. : a number or a product of a number and variables raised . to a power.. Polynomial. : a finite sum of terms of the form . . A Reminiscence 1980-1988. Alexander Morgan. Part of the Prehistory of Applied Algebraic Geometry. A Series of (Fortunate) Unlikely Events. Intellectual epidemiology: . Idea originates with “case zero”. Section 2.4. Terms. Divisor: . Quotient: . Remainder:. Dividend: . PF. FF .  . Long Division. Use long division to find . divided by . ..  . Division Algorithm for Polynomials. Let . and . be polynomials with the degree of . Standard 15. Graph and analyze polynomial and radical functions to determine:. Domain and range. X and y intercepts. Maximum and minimum values. Intervals of increasing and decreasing. End behavior. With the function: f(x) = . 10 Bat Algorithms Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, 2014 The bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang in 2010. 10.1 Echolocation of Bats 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