Max Flow, Min Cut. Maximum Flow and Minimum Cut. Soviet Rail Network, Minimum Cut Problem


 Lynette Stevenson
 2 years ago
 Views:
Transcription
1 Maximum Flow and Minimum u Max Flow, Min u Max flow and min cu. Two very rich algorihmic problem. ornerone problem in combinaorial opimizaion. eauiful mahemaical dualiy. Minimum cu Maximum flow Maxflow mincu heorem FordFulkeron augmening pah algorihm dmondkarp heuriic iparie maching Nonrivial applicaion / reducion. Nework conneciviy. iparie maching. aa mining. Openpi mining. irline cheduling. Image proceing. Projec elecion. aeball eliminaion. Nework reliabiliy. ecuriy of aiical daa. iribued compuing. galiarian able maching. iribued compuing. Many many more... Princeon Univeriy O lgorihm and aa rucure pring Kevin Wayne hp:// ovie Rail Nework, Minimum u Problem Nework: abracion for maerial FLOWING hrough he edge. ireced graph. apaciie on edge. ource node, ink node. Min cu problem. elee "be" e of edge o diconnec from. ource ink capaciy ource: On he hiory of he ranporaion and maximum flow problem. lexander chrijver in Mah Programming, :,.
2 u u cu i a node pariion (, T) uch ha i in and i in T. capaciy(, T) = um of weigh of edge leaving. cu i a node pariion (, T) uch ha i in and i in T. capaciy(, T) = um of weigh of edge leaving. apaciy = apaciy = Minimum u Problem Maximum Flow Problem cu i a node pariion (, T) uch ha i in and i in T. capaciy(, T) = um of weigh of edge leaving. Min cu problem. Find an  cu of minimum capaciy. Nework: abracion for maerial FLOWING hrough he edge. ireced graph. ame inpu a min cu problem apaciie on edge. ource node, ink node. Max flow problem. ign flow o edge o a o: qualize inflow and ouflow a every inermediae verex. Maximize flow en from o. ource capaciy ink apaciy =
3 Flow Flow flow f i an aignmen of weigh o edge o ha: apaciy: f(e) u(e). Flow conervaion: flow leaving v = flow enering v. excep a or flow f i an aignmen of weigh o edge o ha: apaciy: f(e) u(e). Flow conervaion: flow leaving v = flow enering v. excep a or capaciy flow Value = capaciy flow Value = Maximum Flow Problem Flow and u Max flow problem: find flow ha maximize ne flow ino ink. Obervaion. Le f be a flow, and le (, T) be any  cu. Then, he ne flow en acro he cu i equal o he amoun reaching. capaciy flow Value = Value =
4 Flow and u Flow and u Obervaion. Le f be a flow, and le (, T) be any  cu. Then, he ne flow en acro he cu i equal o he amoun reaching. Obervaion. Le f be a flow, and le (, T) be any  cu. Then, he ne flow en acro he cu i equal o he amoun reaching. Value = Value = Flow and u Max Flow and Min u Obervaion. Le f be a flow, and le (, T) be any  cu. Then he value of he flow i a mo he capaciy of he cu. Obervaion. Le f be a flow, and le (, T) be an  cu whoe capaciy equal he value of f. Then f i a max flow and (, T) i a min cu. u capaciy = Flow value u capaciy = Flow value Flow value =
5 MaxFlow Minu Theorem Toward an lgorihm Maxflow mincu heorem. (FordFulkeron, ): In any nework, he value of max flow equal capaciy of min cu. Proof IOU: we find flow and cu uch ha Obervaion applie. Find  pah where each arc ha f(e) < u(e) and "augmen" flow along i. Min cu capaciy = Max flow value = flow Flow value = capaciy Toward an lgorihm Toward an lgorihm Find  pah where each arc ha f(e) < u(e) and "augmen" flow along i. Greedy algorihm: repea unil you ge uck. Find  pah where each arc ha f(e) < u(e) and "augmen" flow along i. Greedy algorihm: repea unil you ge uck. Fail: need o be able o "backrack." flow Flow value = flow Flow value = capaciy X X X capaciy X X X oleneck capaciy of pah = Flow value =
6 Reidual Graph ugmening Pah Original graph. Flow f(e). dge e = vw v flow = f(e) capaciy = u(e) w ugmening pah = pah in reidual graph. Increae flow along forward edge. ecreae flow along backward edge. Reidual edge. dge e = vw or wv. "Undo" flow en. Reidual graph. ll he edge ha have ricly poiive reidual capaciy. v reidual capaciy = u(e) f(e) w reidual capaciy = f(e) reidual original X X X X X ugmening Pah FordFulkeron ugmening Pah lgorihm Obervaion. If augmening pah, hen no ye a max flow. Q. If no augmening pah, i i a max flow? FordFulkeron algorihm. Generic mehod for olving max flow. reidual while (here exi an augmening pah) { Find augmening pah P ompue boleneck capaciy of P ugmen flow along P original Flow value = X X X X X Queion. oe hi lead o a maximum flow? ye How do we find an augmening pah?  pah in reidual graph How many augmening pah doe i ake? How much effor do we pending finding a pah?
7 MaxFlow Minu Theorem Proof of MaxFlow Minu Theorem ugmening pah heorem. flow f i a max flow if and only if here are no augmening pah. Maxflow mincu heorem. The value of he max flow i equal o he capaciy of he min cu. We prove boh imulaneouly by howing he following are equivalen: (i) f i a max flow. (ii) There i no augmening pah relaive o f. (iii) There exi a cu whoe capaciy equal he value of f. (i) (ii) equivalen o no (ii) no (i), which wa Obervaion (ii) (iii) nex lide (iii) (i) hi wa Obervaion (ii) (iii). If here i no augmening pah relaive o f, hen here exi a cu whoe capaciy equal he value of f. Proof. Le f be a flow wih no augmening pah. Le be e of verice reachable from in reidual graph. conain ; ince no augmening pah, doe no conain all edge e leaving in original nework have f(e) = u(e) all edge e enering in original nework have f(e) = f e ou of e ou of f ( e) u( e) capaciy (, T) e in o f ( e) T reidual nework Max Flow Nework Implemenaion FordFulkeron lgorihm: Implemenaion dge in original graph may correpond o or reidual edge. May need o ravere edge e = vw in forward or revere direcion. Flow = f(e), capaciy = u(e). Iner wo copie of each edge, one in adjacency li of v and one in w. FordFulkeron main loop. // while here exi an augmening pah, ue i while (augpah()) { public cla dge { privae in v, w; privae in cap; privae in flow; // from, o // capaciy from v o w // flow from v o w public dge(in v, in w, in cap) {... public in cap() { reurn cap; public in flow() { reurn flow; public boolean from(in v) { reurn hi.v == v; public in oher(in v) { reurn from(v)? hi.w : hi.v; public in capro(in v) { reurn from(v)? flow : cap  flow; public void addflowro(in v, in d) { flow += from(v)? d : d; // compue boleneck capaciy in bole = INFINITY; for (in v = ; v!= ; v = T(v)) bole = Mah.min(bole, pred[v].capro(v)); // augmen flow for (in v = ; v!= ; v = T(v)) pred[v].addflowro(v, bole); // keep rack of oal flow en from o value += bole;
8 FordFulkeron lgorihm: nalyi hooing Good ugmening Pah umpion: all capaciie are ineger beween and U. Ue care when elecing augmening pah. Invarian: every flow value and every reidual capaciie remain an ineger hroughou he algorihm. Theorem: he algorihm erminae in a mo f * V U ieraion. orollary: if U =, hen algorihm run in V ieraion. no polynomial in inpu ize! Inegraliy heorem: if all arc capaciie are ineger, hen here exi a max flow f for which every flow value i an ineger. Original Nework hooing Good ugmening Pah hooing Good ugmening Pah Ue care when elecing augmening pah. Ue care when elecing augmening pah. X X X Original Nework Original Nework
9 hooing Good ugmening Pah hooing Good ugmening Pah Ue care when elecing augmening pah. Ue care when elecing augmening pah. X X X Original Nework Original Nework ieraion poible! hooing Good ugmening Pah hore ugmening Pah Ue care when elecing augmening pah. ome choice lead o exponenial algorihm. lever choice lead o polynomial algorihm. Opimal choice for real world problem??? eign goal i o chooe augmening pah o ha: an find augmening pah efficienly. Few ieraion. hooe augmening pah wih: dmondkarp () Fewe number of arc. (hore pah) Max boleneck capaciy. (fae pah) hore augmening pah. ay o implemen wih F. Find augmening pah wih fewe number of arc. while (!q.impy()) { in v = q.dequeue(); InIeraor i = G.neighbor(v); while(i.hanex()) { dge e = i.nex(); in w = e.oher(v); if (e.capro(w) > ) { // i vw a reidual edge? if (w[w] > w[v] + ) { w[w] = w[v] + ; pred[w] = e; // keep rack of hore pah q.enqueue(w); reurn (w[] < INFINITY); // i here an augmening pah?
10 hore ugmening Pah nalyi Fae ugmening Pah Lengh of hore augmening pah increae monoonically. ricly increae afer a mo augmenaion. mo V oal augmening pah. O( V) running ime. Fae augmening pah. Find augmening pah whoe boleneck capaciy i maximum. eliver mo amoun of flow o ink. olve uing ijkrayle (PF) algorihm. X v reidual capaciy w if (w[w] < Mah.min(w[v], e.capro(w)) { w[w] = Mah.min(w[v], e.capro(w)); pred[w] = v; Finding a fae pah. O( log V) per augmenaion wih binary heap. Fac. O( log U) augmenaion if capaciie are beween and U. hooing an ugmening Pah Hiory of Worae Running Time hooing an augmening pah. ny pah will do wide laiude in implemening FordFulkeron. Generic prioriy fir earch. ome choice lead o good worcae performance. hore augmening pah fae augmening pah variaion on a heme: PF verage cae no well underood. Reearch challenge. Pracice: olve max flow problem on real nework in linear ime. Theory: prove i for worcae nework. Year... icoverer Mehod ympoic Time anzig implex V U Ford, Fulkeron ugmening pah V U dmondkarp hore pah V dmondkarp Max capaciy log U ( + V log V) iniz Improved hore pah V dmondkarp, iniz apaciy caling log U inizgabow Improved capaciy caling V log U Karzanov Preflowpuh V leaortarjan ynamic ree V log V GoldbergTarjan FIFO preflowpuh V log (V / ) GoldbergRao Lengh funcion / log (V / ) log U V / log (V / ) log U rc capaciie are beween and U.
11 n pplicaion iparie Maching Jon placemen. ompanie make job offer. uden have job choice. an we fill every job? iparie maching. Inpu: undireced and biparie graph G. e of edge M i a maching if each verex appear a mo once. Max maching: find a max cardinaliy maching. an we employ every uden? licedobe obyahoo arolhp avepple lizaim Frankun Maching M , ,  L R iparie Maching iparie Maching iparie maching. Inpu: undireced and biparie graph G. e of edge M i a maching if each verex appear a mo once. Max maching: find a max cardinaliy maching. Reduce o max flow. reae a direced graph G'. irec all arc from L o R, and give infinie (or uni) capaciy. dd ource, and uni capaciy arc from o each node in L. dd ink, and uni capaciy arc from each node in R o. L R Maching M , , ,  L R G G'
12 iparie Maching: Proof of orrecne iparie Maching: Proof of orrecne laim. Maching in G of cardinaliy k induce flow in G' of value k. Given maching M = { , ,  of cardinaliy. onider flow f ha end uni along each of pah: f i a flow, and ha cardinaliy. laim. Flow f of value k in G' induce maching of cardinaliy k in G. y inegraliy heorem, here exi / valued flow f of value k. onider M = e of edge from L o R wih f(e) =. each node in L and R inciden o a mo one edge in M M = k L R L R G G' G G' Reducion Reducion. Given an inance of biparie maching. Tranform i o a max flow problem. olve max flow problem. Tranform max flow oluion o biparie maching oluion. Iue. How expenive i ranformaion? O( + V) I i beer o olve problem direcly? O( V / ) biparie maching oom line: max flow i an exremely rich problemolving model. Many imporan pracical problem reduce o max flow. We know good algorihm for olving max flow problem.
Chapter 13. Network Flow III Applications. 13.1 Edge disjoint paths. 13.1.1 Edgedisjoint paths in a directed graphs
Chaper 13 Nework Flow III Applicaion CS 573: Algorihm, Fall 014 Ocober 9, 014 13.1 Edge dijoin pah 13.1.1 Edgedijoin pah in a direced graph 13.1.1.1 Edge dijoin pah queiong: graph (dir/undir)., : verice.
More informationHow Much Can Taxes Help Selfish Routing?
How Much Can Taxe Help Selfih Rouing? Tim Roughgarden (Cornell) Join wih Richard Cole (NYU) and Yevgeniy Dodi (NYU) Selfih Rouing a direced graph G = (V,E) a ource and a deinaion one uni of raffic from
More informationOn the Connection Between MultipleUnicast Network Coding and SingleSource SingleSink Network Error Correction
On he Connecion Beween MulipleUnica ework Coding and SingleSource SingleSink ework Error Correcion Jörg Kliewer JIT Join work wih Wenao Huang and Michael Langberg ework Error Correcion Problem: Adverary
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationStock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783
Sock raing wih Recurren Reinforcemen Learning (RRL) CS9 Applicaion Projec Gabriel Molina, SUID 555783 I. INRODUCION One relaively new approach o financial raing is o use machine learning algorihms o preic
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationOptimal Investment and Consumption Decision of Family with Life Insurance
Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker
More informationThe Role of Science and Mathematics in Software Development
The cienific mehod i eenial in applicaion of compuaion A peronal opinion formed on he bai of decade of experience a a The Role of Science and Mahemaic in Sofware Developmen CS educaor auhor algorihm deigner
More informationFortified financial forecasting models: nonlinear searching approaches
0 Inernaional Conference on Economic and inance Reearch IPEDR vol.4 (0 (0 IACSIT Pre, Singapore orified financial forecaing model: nonlinear earching approache Mohammad R. Hamidizadeh, Ph.D. Profeor,
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationThe Role of the Scientific Method in Software Development. Robert Sedgewick Princeton University
The Role of he Scienific Mehod in Sofware Developmen Rober Sedgewick Princeon Univeriy The cienific mehod i neceary in algorihm deign and ofware developmen Scienific mehod creae a model decribing naural
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationGloballyOptimal Greedy Algorithms for Tracking a Variable Number of Objects
GloballyOpimal Greedy Algorihm for Tracking a Variable Number of Objec Hamed Piriavah Deva Ramanan Charle C. Fowlke Deparmen of Compuer Science, Univeriy of California, Irvine {hpiriav,dramanan,fowlke}@ic.uci.edu
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationTopK Structural Diversity Search in Large Networks
TopK Srucural Diversiy Search in Large Neworks Xin Huang, Hong Cheng, RongHua Li, Lu Qin, Jeffrey Xu Yu The Chinese Universiy of Hong Kong Guangdong Province Key Laboraory of Popular High Performance
More informationHeat demand forecasting for concrete district heating system
Hea demand forecaing for concree diric heaing yem Bronilav Chramcov Abrac Thi paper preen he reul of an inveigaion of a model for horerm hea demand forecaing. Foreca of hi hea demand coure i ignifican
More informationSignal Processing and Linear Systems I
Sanford Universiy Summer 214215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 1415, Gibbons
More informationThe Application of Multi Shifts and Break Windows in Employees Scheduling
The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance
More informationMortality Variance of the Present Value (PV) of Future Annuity Payments
Morali Variance of he Presen Value (PV) of Fuure Annui Pamens Frank Y. Kang, Ph.D. Research Anals a Frank Russell Compan Absrac The variance of he presen value of fuure annui pamens plas an imporan role
More informationSinglemachine Scheduling with Periodic Maintenance and both Preemptive and. Nonpreemptive jobs in Remanufacturing System 1
Absrac number: 050407 Singlemachine Scheduling wih Periodic Mainenance and boh Preempive and Nonpreempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationLecture 15 Isolated DCDC converters
ELEC440/940 Lecure 15 olae CC converer Ofen, he oupu C volage fro a CC converer u be iolae fro he inpu AC upply. C power upplie for appliance an equipen are goo exaple. i avanageou o have he iolaion
More informationA Comparative Study of Linear and Nonlinear Models for Aggregate Retail Sales Forecasting
A Comparaive Sudy of Linear and Nonlinear Model for Aggregae Reail Sale Forecaing G. Peer Zhang Deparmen of Managemen Georgia Sae Univeriy Alana GA 30066 (404) 6514065 Abrac: The purpoe of hi paper i
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationTHE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS
VII. THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS The mos imporan decisions for a firm's managemen are is invesmen decisions. While i is surely
More informationOptimal Path Routing in Single and Multiple Clock Domain Systems
IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN, TO APPEAR. 1 Opimal Pah Rouing in Single and Muliple Clock Domain Syem Soha Haoun, Senior Member, IEEE, Charle J. Alper, Senior Member, IEEE ) Abrac Shrinking
More informationQuality Assurance in Software Development
Insiue for Sofware Technology Qualiy Assurance in Sofware Developmen Qualiässicherung in der Sofwareenwicklung A.o.Univ.Prof. Dipl.Ing. Dr. Bernhard Aichernig Insiu für Sofwareechnologie (IST) TU Graz
More informationMultiprocessor SystemsonChips
Par of: Muliprocessor SysemsonChips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,
More informationSTABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS
STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS ELLIOT ANSHELEVICH, DAVID KEMPE, AND JON KLEINBERG Absrac. In he dynamic load balancing problem, we seek o keep he job load roughly
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationBetter Bounds for Online Load Balancing on Unrelated Machines
Beer Bound for Online Load Balancing on Unrelaed Machine Ioanni Caragianni Abrac We udy he roblem of cheduling ermanen ob on unrelaed machine when he obecive i o minimize he L norm of he machine load.
More informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 073807 Ifeachor
More informationSmooth Priorities for MultiProduct Inventory Control
Smooh rioriies for Muliroduc Invenory Conrol Francisco José.A.V. Mendonça*. Carlos F. Bispo** *Insiuo Superior Técnico  Universidade Técnica de Lisboa (email:favm@mega.is.ul.p) ** Insiuo de Sisemas e
More informationDiagnostic Examination
Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)
More informationOnline Convex Programming and Generalized Infinitesimal Gradient Ascent
Online Convex Programming and Generalized Infiniesimal Gradien Ascen Marin Zinkevich Carnegie Mellon Universiy, 5000 Forbes Avenue, Pisburgh, PA 1513 USA maz@cs.cmu.edu Absrac Convex programming involves
More informationTask is a schedulable entity, i.e., a thread
RealTime Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T:  s: saring poin  e: processing ime of T  d: deadline of T  p: period of T Periodic ask T
More informationINTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails
INTRODUCTION TO EMAIL MARKETING PERSONALIZATION How o increase your sales wih personalized riggered emails ECOMMERCE TRIGGERED EMAILS BEST PRACTICES Triggered emails are generaed in real ime based on each
More informationChapter 6 Interest Rates and Bond Valuation
Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Longerm debloosely, bonds wih a mauriy of one year or more Shorerm debless han a year o mauriy, also called unfunded deb Bondsricly
More informationAP Calculus AB 2010 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationName: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling
Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: Solving Exponenial Equaions (The Mehod of Common Bases) Solving Exponenial Equaions (Using Logarihms)
More informationPhysical Topology Discovery for Large MultiSubnet Networks
Phyical Topology Dicovery for Large MuliSubne Nework Yigal Bejerano, Yuri Breibar, Mino Garofalaki, Rajeev Raogi Bell Lab, Lucen Technologie 600 Mounain Ave., Murray Hill, NJ 07974. {bej,mino,raogi}@reearch.belllab.com
More informationEmpirical heuristics for improving Intermittent Demand Forecasting
Empirical heuriic for improving Inermien Demand Forecaing Foio Peropoulo 1,*, Konanino Nikolopoulo 2, Georgio P. Spihouraki 1, Vailio Aimakopoulo 1 1 Forecaing & Sraegy Uni, School of Elecrical and Compuer
More informationMaking a Faster Cryptanalytic TimeMemory TradeOff
Making a Faser Crypanalyic TimeMemory TradeOff Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch
More informationFair Stateless Model Checking
Fair Saeless Model Checking Madanlal Musuvahi Shaz Qadeer Microsof Research {madanm,qadeer@microsof.com Absrac Saeless model checking is a useful saespace exploraion echnique for sysemaically esing complex
More informationDividend taxation, share repurchases and the equity trap
Working Paper 2009:7 Deparmen of Economic Dividend axaion, hare repurchae and he equiy rap Tobia Lindhe and Jan Söderen Deparmen of Economic Working paper 2009:7 Uppala Univeriy May 2009 P.O. Box 53 ISSN
More informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prinou should hae 1 quesions. Muliplechoice quesions may coninue on he ne column or page find all choices before making your selecion. The
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More information1 HALFLIFE EQUATIONS
R.L. Hanna Page HALFLIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of halflives, and / log / o calculae he age (# ears): age (halflife)
More informationDynamic programming models and algorithms for the mutual fund cash balance problem
Submied o Managemen Science manuscrip Dynamic programming models and algorihms for he muual fund cash balance problem Juliana Nascimeno Deparmen of Operaions Research and Financial Engineering, Princeon
More informationOn Certain Properties of Random Apollonian Networks
On Cerain Properies of Random Apollonian Neworks Alan Frieze, Charalampos E. Tsourakakis Deparmen of Mahemaical Sciences, Carnegie Mellon Universiy, USA af1p@random.mah.cmu.edu, csourak@mah.cmu.edu Absrac.
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationCALCULATION OF OMX TALLINN
CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, realime and closing value of he Index...3 3.2. Index
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationPlanning Demand and Supply in a Supply Chain. Forecasting and Aggregate Planning
Planning Demand and Supply in a Supply Chain Forecasing and Aggregae Planning 1 Learning Objecives Overview of forecasing Forecas errors Aggregae planning in he supply chain Managing demand Managing capaciy
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationNASDAQ100 Futures Index SM Methodology
NASDAQ100 Fuures Index SM Mehodology Index Descripion The NASDAQ100 Fuures Index (The Fuures Index ) is designed o rack he performance of a hypoheical porfolio holding he CME NASDAQ100 Emini Index
More informationSampling TimeBased Sliding Windows in Bounded Space
Sampling TimeBased Sliding Windows in Bounded Space Rainer Gemulla Technische Universiä Dresden 01062 Dresden, Germany gemulla@inf.udresden.de Wolfgang Lehner Technische Universiä Dresden 01062 Dresden,
More informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationStatistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by SongHee Kim and Ward Whitt
Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by SongHee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 1799
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More informationQSAC: Toward QoS Optimized Service Automatic Composition *
QSAC: Toward QoS Opimized Service Auomaic Composiion * Hanhua Chen, Hai Jin, Xiaoming Ning, Zhipeng Lü Cluser and Grid Compuing Lab Huazhong Universiy of Science and Technology, Wuhan, 4374, China Email:
More informationThe Roos of Lisp paul graham Draf, January 18, 2002. In 1960, John McCarhy published a remarkable paper in which he did for programming somehing like wha Euclid did for geomery. 1 He showed how, given
More informationCHAPTER FIVE. Solutions for Section 5.1
CHAPTER FIVE 5. SOLUTIONS 87 Soluions for Secion 5.. (a) The velociy is 3 miles/hour for he firs hours, 4 miles/hour for he ne / hour, and miles/hour for he las 4 hours. The enire rip lass + / + 4 = 6.5
More informationQualityOfService Class Specific Traffic Matrices in IP/MPLS Networks
ualiyofservice Class Specific Traffic Marices in IP/MPLS Neworks Sefan Schnier Deusche Telekom, TSysems D4 Darmsad +4 sefan.schnier@sysems.com Franz Harleb Deusche Telekom, TSysems D4 Darmsad +4
More informationQualityOfService Class Specific Traffic Matrices in IP/MPLS Networks
ualiyofservice Class Specific Traffic Marices in IP/MPLS Neworks Sefan Schnier Deusche Telekom, TSysems D4 Darmsad +4 sefan.schnier@sysems.com Franz Harleb Deusche Telekom, TSysems D4 Darmsad +4
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationAlgorithm Design and Analysis
Algorithm Design and Analysis LECTURE 27 Approximation Algorithms Load Balancing Weighted Vertex Cover Reminder: Fill out SRTEs online Don t forget to click submit Sofya Raskhodnikova 12/6/2011 S. Raskhodnikova;
More informationNanocubes for RealTime Exploration of Spatiotemporal Datasets
Nanocube for RealTime Exploraion of Spaioemporal Daae Lauro Lin, Jame T Kloowki, and arlo Scheidegger Fig 1 Example viualizaion of 210 million public geolocaed Twier po over he coure of a year The daa
More informationThe option pricing framework
Chaper 2 The opion pricing framework The opion markes based on swap raes or he LIBOR have become he larges fixed income markes, and caps (floors) and swapions are he mos imporan derivaives wihin hese markes.
More informationPremium Income of Indian Life Insurance Industry
Premium Income of Indian Life Insurance Indusry A Toal Facor Produciviy Approach Ram Praap Sinha* Subsequen o he passage of he Insurance Regulaory and Developmen Auhoriy (IRDA) Ac, 1999, he life insurance
More informationGenetic Algorithm Search for Predictive Patterns in Multidimensional Time Series
Geneic Algorihm Search for Predicive Paerns in Mulidimensional Time Series Arnold Polanski School of Managemen and Economics Queen s Universiy of Belfas 25 Universiy Square Belfas BT7 1NN, Unied Kingdom
More informationPerformance Center Overview. Performance Center Overview 1
Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener
More informationOn the degrees of irreducible factors of higher order Bernoulli polynomials
ACTA ARITHMETICA LXII.4 (1992 On he degrees of irreducible facors of higher order Bernoulli polynomials by Arnold Adelberg (Grinnell, Ia. 1. Inroducion. In his paper, we generalize he curren resuls on
More informationImprovement of a TCP Incast Avoidance Method for Data Center Networks
Improvemen of a Incas Avoidance Mehod for Daa Cener Neworks Kazuoshi Kajia, Shigeyuki Osada, Yukinobu Fukushima and Tokumi Yokohira The Graduae School of Naural Science and Technology, Okayama Universiy
More information13. a. If the oneyear discount factor is.905, what is the oneyear interest rate?
CHAPTER 3: Pracice quesions 3. a. If he oneyear discoun facor is.905, wha is he oneyear ineres rae? = DF = + r 0.905 r = 0.050 = 0.50% b. If he woyear ineres rae is 0.5 percen, wha is he woyear discoun
More informationTrends in TCP/IP Retransmissions and Resets
Trends in TCP/IP Reransmissions and Reses Absrac Concordia Chen, Mrunal Mangrulkar, Naomi Ramos, and Mahaswea Sarkar {cychen, mkulkarn, msarkar,naramos}@cs.ucsd.edu As he Inerne grows larger, measuring
More informationInfrastructure and Evolution in Division of Labour
Infrarucure and Evoluion in Diviion of Labour Mei Wen Monah Univery (Thi paper ha been publihed in RDE. (), 906) April 997 Abrac Thi paper udie he relaionhip beween infrarucure ependure and endogenou
More informationInformation Theoretic Approaches for Predictive Models: Results and Analysis
Informaion Theoreic Approaches for Predicive Models: Resuls and Analysis Monica Dinculescu Supervised by Doina Precup Absrac Learning he inernal represenaion of parially observable environmens has proven
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More informationThe Equivalent Loan Principle and the Value of Corporate Promised Cash Flows. David C. Nachman*
he Equivalen Loan Principle and he Value of Corporae Promied Cah Flow by David C. Nachman* Revied February, 2002 *J. Mack Robinon College of Buine, Georgia Sae Univeriy, 35 Broad Sree, Alana, GA 303033083.
More informationEfficient Onetime Signature Schemes for Stream Authentication *
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING, 61164 (006) Efficien Oneime Signaure Schemes for Sream Auhenicaion * YONGSU PARK AND YOOKUN CHO + College of Informaion and Communicaions Hanyang Universiy
More informationEnergy and Performance Management of Green Data Centers: A Profit Maximization Approach
Energy and Performance Managemen of Green Daa Ceners: A Profi Maximizaion Approach Mahdi Ghamkhari, Suden Member, IEEE, and Hamed MohsenianRad, Member, IEEE Absrac While a large body of work has recenly
More informationA Load Balancing Method in Downlink LTE Network based on Load Vector Minimization
A Load Balancing Mehod in Downlink LTE Nework based on Load Vecor Minimizaion Fanqin Zhou, Lei Feng, Peng Yu, and Wenjing Li Sae Key Laboraory of Neworking and Swiching Technology, Beijing Universiy of
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationThe Binary Blocking Flow Algorithm. Andrew V. Goldberg Microsoft Research Silicon Valley www.research.microsoft.com/ goldberg/
The Binary Blocking Flow Algorithm Andrew V. Goldberg Microsoft Research Silicon Valley www.research.microsoft.com/ goldberg/ Why this MaxFlow Talk? The result: O(min(n 2/3, m 1/2 )mlog(n 2 /m)log(u))
More informationRobust Bandwidth Allocation Strategies
Robu Bandwidh Allocaion Sraegie Oliver Heckmann, Jen Schmi, Ralf Seinmez Mulimedia Communicaion Lab (KOM), Darmad Univeriy of Technology Merckr. 25 D64283 Darmad Germany {Heckmann, Schmi, Seinmez}@kom.udarmad.de
More informationPATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM
PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM WILLIAM L. COOPER Deparmen of Mechanical Engineering, Universiy of Minnesoa, 111 Church Sree S.E., Minneapolis, MN 55455 billcoop@me.umn.edu
More informationModule 3 Design for Strength. Version 2 ME, IIT Kharagpur
Module 3 Design for Srengh Lesson 2 Sress Concenraion Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress
More informationE0 370 Statistical Learning Theory Lecture 20 (Nov 17, 2011)
E0 370 Saisical Learning Theory Lecure 0 (ov 7, 0 Online Learning from Expers: Weighed Majoriy and Hedge Lecurer: Shivani Agarwal Scribe: Saradha R Inroducion In his lecure, we will look a he problem of
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 14, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
More informationHow has globalisation affected inflation dynamics in the United Kingdom?
292 Quarerly Bullein 2008 Q3 How ha globaliaion affeced inflaion dynamic in he Unied Kingdom? By Jennifer Greenlade and Sephen Millard of he Bank Srucural Economic Analyi Diviion and Chri Peacock of he
More informationStock option grants have become an. Final Approval Copy. Valuation of Stock Option Grants Under Multiple Severance Risks GURUPDESH S.
Valuaion of Sock Opion Gran Under Muliple Severance Rik GURUPDESH S. PANDHER i an aian profeor in he deparmen of finance a DePaul Univeriy in Chicago, IL. gpandher@depaul.edu GURUPDESH S. PANDHER Execuive
More informationCalculation of variable annuity market sensitivities using a pathwise methodology
cuing edge Variable annuiie Calculaion of variable annuiy marke eniiviie uing a pahwie mehodology Under radiional finie difference mehod, he calculaion of variable annuiy eniiviie can involve muliple Mone
More information