with BDDs **and** a clever context numbering scheme –Inclusion-based pointer **analysis** 10 14 contexts, 19 minutes –Generates all answers 13 Contribution (2) BDD hacking is complicated bddbddb (BDD-based deductive database) Pointer **analysis** in 6 lines **of** Datalog Automatic / Java projects on SourceForge –Real programs with 100K+ users each Using automatic bddbddb solver –Each **analysis** only a few lines **of** code –Easy to try new **algorithms**, new queries Test system: –Pentium 4 2.2GHz, 1GB RAM –RedHat Fedora Core 1,/

**and** **Analysis** Toolkit for ISIS data Agenda TimeItem 2:00Introduction 2:15Python Overview **and** Running **Algorithms** 2:30Exercise 1: Removing the Prompt pulse 3:00Generating **and** generalising scripts 3:10Exercise 2: Create a reusable script 3:40Manipulating graphs **and**//URD.doc Architectural **Design** Document –http://svn.mantidproject.org/mantid/trunk/Documents/**Design**/Architecture%20Des ign%20Document.dochttp://svn.mantidproject.org/mantid/trunk/Documents/**Design**/Architecture%20Des ign%/**of** the line **and** add “;c:python25”

modes Gauge topology: Dirac eq. Inverse problems Optimal **design** Integral equations Statistical mechanics Massive parallel processing *Rigorous quantitative **analysis** (1986) FAS (1975) Within one solver (1977,1982) interpolation (order l+p) to a new grid interpolation (order m) **of** corrections relaxation sweeps algebraic error < truncation error residual transfer enough sweeps or direct solver * *** Full MultiGrid (FMG) **algorithm**... * h0h0 h 0 /2 h 0 /4/

develop a useful insight into recurrences. This insight will help you fine-tune the previous inefficient **algorithm** **and** eventually lead to **design** (**and** **analysis**) **of** a more efficient **algorithm** for min-cut. 16 Common recurrences 17 Common recurrences 18 FASTER MIN-CUT **ALGORITHM** 19 Revisiting **algorithm** for min-cut 20 We shall modify this **algorithm** to improve its success probability. But we shall not allow any significant blow up in/

**Design** **and** **Analysis** **of** **Algorithms** Heapsort Haidong Xue Summer 2012, at GSU Max-Heap A complete binary tree, **and** … Yes No every level is completely filled, except possibly the last, which is filled from left to right Max-Heap /. From the last element to the second{ exchange (current, root); l--; Max-Heapify(A, root, l); } Let’s try it **Analysis** **of** Heapsort Input: array A Output: sorted array A **Algorithm**: 1. Build-Max-Heap(A) 2. Last node index l = A’s last node index 3. From the last element to the second/

Learn fundamental **algorithms** **and** data structures Find **and** **design** new ones Reason about them Use them Prepare you for more CS Lectures 10 Homeworks (30%) 4 Projects (30%) 2 Exams (30%) Sections (10%) req’d! Keep up with website! Reading: Dasgupta **and** readings on blog What are we learning aboot? Basics: Big-O, Recurrence, Mathematical Induction, Hashing Methods: Greedy **Algorithms**, Divide **and** Conquer, Dynamic Programming **Analysis** **of** **Algorithms**: Time Complexity/

ibn Mūsā al-Khwārizmī Brahmagupta 0628 Algoritmi de numero Indorum. Anthyphairesis Euclidean **algorithm** Euclids Elements -0299 Gottfried Wilhelm von Leibniz Calculus ratiocinator 1680 Augusta Ada King, Countess **of** Lovelace 19 th Cent. **Algorithms** Time **and** space complexity **Analysis** Pseudocode **Design** Data Types What is a data type? A way **of** classifying pieces **of** information Useful for computers Examples Primitive Integers, reals, boolean(?) Composite Arrays, struct, unions/

Software Challenge: The Big Picture The Software Challenge: Create even larger more efficient **algorithms**: **Design** & **Analysis** **of** **Algorithms** Create programs that meet **design** specs: Program Verification Create readable & understandable programs: Program Documentation Create platform independent programs: Portability The Big Picture Shudder !!! To be **and** to stay competitive, we need learn to “think ahead **of** the curve” This means continually learning how to use more sophisticated approaches to the/

Trade ä **Algorithm** **Design** Patterns ä dynamic programming, greedy, approximation **algorithms** ä Advanced **Analysis** Techniques ä asymptotic **analysis** ä Theoretical Computer Science principles ä NP-completeness, hardness ä Advanced Data Structures ä interval trees, binomial heaps Asymptotic Growth **of** Functions Summations Recurrences Sets Probability MATH Proofs Calculus Combinations Logarithms Number Theory Geometry Trigonometry Complex Numbers Permutations Linear Algebra Polynomials Prerequisites ä 91.500 **and** 91/

Estimation at late placement stages using probabilistic **analysis** Mayrhofer **and** Lauther, ICCAD’90. Partitioning based method Cheng, ICCAD/**and** double expansion Comparison between single expansion **and** double expansion circuit: ibm02 International Conference on Computer-Aided **Design** San Jose, CA Nov. 2001ER UCLA UCLA 22SummarySummary Congestion reduction as a post-processing ILP based congestion reduction control Approximation **algorithms** with good bound Future Work Extend the approach using ILP instead **of**/

UMass Lowell Computer Science 91.503 **Analysis** **of** **Algorithms** Prof. Karen Daniels Fall, 2002 Lecture 1 (Part 1) Introduction/Overview Tuesday, 9/3/02 Web Page http://www.cs.uml.edu/~kdaniels/courses/ALG_503.html Web Page Nature **of** the Course ä Core course: required for all CS graduate students ä Advanced **algorithms** ä Builds on undergraduate **algorithms** 91.404 ä No programming required ä “Pencil-**and**-paper” exercises ä Lectures supplemented by: ä Programs/

) Common Computational Geometry Structures Voronoi Diagram Convex Hull New Point source: O’Rourke, Computational Geometry in C Delaunay Triangulation Sample Tools **of** the Trade **Algorithm** **Design** Patterns/Techniques: binary searchdivide-**and**-conquerduality randomizationsweep-line derandomizationparallelism **Algorithm** **Analysis** Techniques: asymptotic **analysis**, amortized **analysis** Data Structures: winged-edge, quad-edge, range tree, kd-tree Theoretical Computer Science principles: NP-completeness, hardness Growth/

UMass Lowell Computer Science 91.503 **Analysis** **of** **Algorithms** Prof. Karen Daniels Fall, 2004 Lecture 1 (Part 1) Introduction/Overview Wednesday, 9/8/04 Web Page http://www.cs.uml.edu/~kdaniels/courses/ALG_503.html Nature **of** the Course ä Core course: required for all CS graduate students ä Advanced **algorithms** ä Builds on undergraduate **algorithms** 91.404 ä No programming required ä “Pencil-**and**-paper” exercises ä Lectures supplemented by: ä Programs ä Real-world/

UMass Lowell Computer Science 91.503 **Analysis** **of** **Algorithms** Prof. Karen Daniels Spring, 2002 Lecture 1 (Part 1) Introduction/Overview Tuesday, 1/29/02 Web Page http://www.cs.uml.edu/~kdaniels/courses/ALG_503.html Web Page Nature **of** the Course ä Core course: required for all CS graduate students ä Advanced **algorithms** ä Builds on undergraduate **algorithms** 91.404 ä No programming required ä “Pencil-**and**-paper” exercises ä Lectures supplemented by: ä Programs/

phases: –Block **design** –Putting a system together Simulink /VHDL Simulation **Design** Projects –/ decoder –SVD System Integration **and** Simulation Students: Hayun Tang/**Design** a 1.6 Mbps DSSS timing recovery unit Modulation –Length 31 PN code –QPSK symbol constellation System specifications –Maximum frequency offset **of** +/- 200 KHz –Minimum input SNR **of**/**and** Q paths Need 60 dB IRR Adaptation via /**and**/**algorithm** plus soft output Reliability Measure Unit /**algorithm**: forward **and**/**design** flow What did we learn? /

1 GCD The **Design** **and** **Analysis** **of** Computer **Algorithms** 8.8 Greatest common divisors **and** Euclid’s **algorithm** 報告者：張書豪 2 Outline Half GCD Example 3 HGCD **Algorithm** procedure HGCD(a 0,a 1 ) ： If DEG(a 1 ) ≦ DEG(a 0 )/2 then else begin let a 0 =b 0 x m +c 0, where m= **and** DEG(c 0 ) ＜ m ； let a 1 ＝ b 1 x m ＋ c 1,where DEG(c 1 ) DEG(3)/2 下限 →b 0 =(4x 2 -7x+11)x+22 b 1 =(-3/16x-93/16)x-45/8 DEG(1)=DEG(2)/2

1 **Design** **and** **Analysis** **of** **Algorithms** تصميم وتحليل الخوارزميات (311 عال) Chapter 1 Introduction to **Algorithms** 2 Computational problems A computational problem specifies an input-output relationship What does the input look like? What should the output be for each input? Example 1: Input: an integer number n Output: Is the number odd ( هل الرقم فردي أو لا )? true Example 2: Input: array **of** numbers Output: the minimum number in the array Example 3: Input: array **of** numbers/

**Design** **and** **Analysis** **of** **Algorithms** Non-comparison sort (sorting in linear time) Haidong Xue Summer 2012, at GSU Comparison based sorting **Algorithms** that determine sorted order based only on comparisons between the input elements AlgorithmWorst TimeExpected TimeExtra MemoryStable Insertion sortO(1) (in place)Can be Merge sortO(n)Can be Quick sortO(/

**design** **of** a large- scale avionics system Improved deployment **design** reduces: Hardware cost Power consumption Fuel consumption Network load Evolutionary **algorithms** /**and** Douglas C. Schmidt, Deployment Automation with BLITZ, 31st International Conference on Software Engineering, May 16-24, 2009 Vancouver, Canada 10.Brian Dougherty, Jules White, Chris Thompson, & Douglas C. Schmidt, Automating Hardware & Software Evolution **Analysis**, 16th Annual IEEE International Conference & Workshop on the Engineering **of**/

14: Recursion J ava P rogramming: From Problem **Analysis** to Program **Design**, From Problem **Analysis** to Program **Design**, Second Edition Second Edition Java Programming: From Problem **Analysis** to Program **Design**, Second Edition2 Chapter Objectives Learn about recursive definitions. Explore the base case **and** the general case **of** a recursive definition. Learn about recursive **algorithms**. Learn about recursive methods. Become aware **of** direct **and** indirect recursion. Explore how to use recursive methods/

–Limited understanding **of** **algorithms** **Design** Objectives Intended Users & Uses Intended Users & Uses –People in decision-making positions Gain greater understanding **of** methods Gain greater understanding **of** methods –Software Programmers Have background reference information Have background reference information Detailed starting point for developing software Detailed starting point for developing software End Product Description The report will aid individuals in conducting a thorough **analysis** **of** the decision/

**Analysis** **of** Models (**Design**) –**Design**-Space Exploration: Optimize **design**, select best configurations from alternative **designs** Highly scalable using OBDD –Numerical/**Algorithmic** Simulation with Matlab –Multiple-Resolution Performance Simulation with Discrete Event Simulator Model-Integrated **Design** /Pr2.assignees =(P1 i or P2 j ))**and**(Pr2=Pr2 j ) (D1.time - D2.time) < 2 Timing Constraints Constraint Modeling Power Constraints (mode=S2 implies (Proc.Powr<10)) **Design** Space Exploration Behavior Mod. (Hier. Par/

**Analysis** Document (Starting Now) Purpose **of** **Analysis** Do current practices solve the MIF problems? Or are there gaps? –If current practices work, should we standardize them? –If not, can we **design**/ cases (DHCP, DNS, etc.) –Per prefix configuration for default gateway **and** routing? Current IETF Standards The standard data model (MIBs, Netconf schema,/merge info from multiple servers Current IETF Standards (cont) Address selection **algorithm** –MISSING: Policy support, per prefix selection Sockets API –Override /

**and** PARSEC Comparing only shadow value checks 14 Watchpoint-Based Taint **Analysis** 15 19x10x30x207x423x23x 1429x 20% Slowdown 128 entry Range Cache The Need for Many Small Ranges Some watchpoints better suited for ranges 32b Addresses: 2 ranges x 64b each = 16B Some need large # **of**/generic mechanism Numerous SW systems can utilize a well- **designed** WP system In the future: Clear microarchitectural **analysis** More software systems, different **algorithms** 19 20 Thank You BACKUP SLIDES 21 Existing Watchpoint /

.”**Design** **of** Systems: structural approach”, 2004…2008, Moscow Inst. **of** Physics & Technology (State Univ.), Students: IT & Cybernetics (about 350 students), advanced undergrad., in Russian & English (individual / team research projects: applications/real world problems, models, **algorithms**) SOME MY FUNDAMENTALS 1.Learning at 4 levels (from AI) 2.Scale **of** novelty (creation) by Altshuller (TRIZ) 3.Decision cycle (**and** corresponding educational flow) 4.Multi-problem support approach (selection/

1cm2cm 3cm4cm5cm Camera Testing Resolution Test 80x64128x96160x128320x240 Camera Testing Lighting Test Camera Testing Image **analysis** After 3V, we see little variation within histogram Meridian/P Microcontroller C# **and**.NET Micro Framework ARM9 Processor at 100 MHz 27 GPIO pins at 3.3 V Software Architecture Microcontroller Flowchart OCR **Algorithm** 1. Line Recognition 2. Matrix Mapping 3. Weight Multiplication Initial Solenoid Testing S-10/

331 Main Steps in **Algorithm** **Design** Problem Statement **Algorithm** Problem Definition “Implementation” **Analysis** n! Correctness+Runtime **Analysis** Data Structures Where do graphs fit in? Problem Statement **Algorithm** Problem Definition Implementation **Analysis** A tool to define problems Rest **of** the course Problem Statement **Algorithm** Problem Definition Implementation **Analysis** Three general techniques Now: Greedy **Algorithms** Later: Divide **and** Conquer Later: Dynamic Programming Greedy **algorithms** Build the final solution/

2006 2 Outline Introduction Data Reduction **and** **analysis** Library **Design** for DRA Global View **of** DRA Library Class UML Diagram **and** Control Summery Jian Gui WANG Bragg Institute Meeting Java **Algorithm** Library Dec 14 2006 3 Introduction Provide data reduction capability **and** support for data **analysis** tools to the users **of** the OPAL neutron beam instruments DRA library contains data reduction **and** **analysis** **algorithm** modules Provide graphic **and** non-graphic access interface Java/

**of** Induction Able to prove by Induction **Algorithmic** Foundations COMP108 4 (Induction) **Analysis** **of** **Algorithms** After **designing** an **algorithm**, we analyze it. Proof **of** correctness: show that the **algorithm** gives the desired result Time complexity **analysis**: find out how fast the **algorithm** runs Space complexity **analysis**: find out how much memory space the **algorithm** requires Look for improvement: can we improve the **algorithm**/**and** so on...... By principle **of** induction: holds for all +ve integers n **Algorithmic**/

Systems Integration Market **Analysis** UI Gamification UX **Analysis** Quant **Analysis** RELATIONSHIPS Sales Force driven (door to door) Communicate Financial **and** Technological Expertise Reliable online/**and** Commission? Licensing Autotrader **and** Comission? Consultancy in Strategies for Autotrader Strategies Implementation for Autotrader Order Management System Licensing Created by BM|**DESIGN**|ER PARTNERS Brokerage, Asset Management Softwarehouse VALUE PROPOSITION Inovation because we develop better **Algorithms** because **of**/

:= 2 to nt 2 if a i > v then v := a i t 3 return vt 4 Times for each execution **of** each line. ( 각 line 을 하나의 수행으로 볼 때의 시간 ) **Algorithm** Complexity Discrete Mathematics by Yang-Sae Moon Page 6 Complexity **Analysis** **of** Max **Algorithm** (2/2) Worst case execution time: procedure max(a 1, a 2, …, a n : integers) v := a 1/100 ns16 m 40 s 2n2n 1.024 s 10 301,004.5 Gyr n!n!3.63 msOuch! You should carefully **design** **algorithms** **and** write programs! **Algorithm** Complexity Discrete Mathematics by Yang-Sae Moon Page 19 Homework #3/

Zong Woo Geem What is Optimization? Procedure to make a system or **design** as effective, especially the mathematical techniques involved. ( Meta-Heuristics) Finding Best Solution Minimal Cost (**Design**) Minimal Error (Parameter Calibration) Maximal Profit (Management) Maximal Utility (Economics) Types **of** Optimization **Algorithms** Mathematical **Algorithms** Simplex (LP), BFGS (NLP), B&B (DP) Drawbacks **of** Mathematical **Algorithms** LP: Too Ideal (All Linear Functions) NLP: Not for Discrete Var. or/

RISC Region Operations Mgr Region Fault Mgr Runtime **Design** **and** **Analysis** Reconfig Behavior **Algorithm** Fault Behavior Resource Synthesis Performance Simulation Diagnosability **Analysis** Reliability **Analysis** System Models Soft Real-Time Hard Experiment Interface /, marks source memory bank as unused/unavail –GET_LOCAL_STATUS Function: Reports status **of** a resource on a local node –SEND_MESSAGE –RECEIVE_MESSAGE –... Synthesis: **Analysis**/Offline Simulation –Functional (e.g. Matlab) –Performance (Timing, Discrete Event/

case Another **design** paradigm –Use **of** a data structure (heap) to manage information during execution **of** **algorithm** Comparision-based Sorting **Algorithm** **Analysis** **of** Algorithms1 Heap Data Structure **Analysis** **of** Algorithms2 Heap Property **Analysis** **of** Algorithms3 A Heap Example **Analysis** **of** Algorithms4 Heap Data Structure **Analysis** **of** Algorithms5 Heap Operations **Analysis** **of** Algorithms6 Heap Operations **Analysis** **of** Algorithms7 Maintaining Heap **Analysis** **of** Algorithms8 Runtime **Analysis** **of** HEAPIFY **Analysis** **of** Algorithms9/

**Design** & **Analysis** **of** Efficient **Algorithms** Graph **Algorithms** Shortest Path **Algorithms** Fall 2013 Path Finding Problems Many problems in computer science correspond to searching for paths in a graph from a given start node Route planning Packet-switching VLSI layout 6-degrees **of**/2002) Invented concepts **of** structured programming, synchronization, weakest precondition, **and** "semaphores" for controlling computer processes. The Oxford English Dictionary cites his use **of** the words "vector" **and** "stack" in a computing/

Temperature Density Speed Shock wave development inside nozzle Difference **of** inlet stagnation pressure **and** exit pressure Applications Rocket Propulsion Wind Tunnel http://tfm.usc/**of** nozzle parameters Response Surface Evolutionary Based **Algorithm** Particle Swarm (PS) Optimal Solution Manufacturing Dimensional **Analysis** (small scale) True scale versus model Plexiglas **design** Alternative Materials being considered Relevant Standards AS 9100 Quality management **of** aerospace industry Created by SAE – Society **of**/

No high-level geometric primitives Incomplete, invalid, conflicting GATE-540 4 Course Objective Develop **algorithms** for processing **and** **analysis** **of** 3D shapes/geometries How can we make a 3D data/model be usable in your application? GATE-540 5 3D Applications 3D Data can be employed in many domains such as: –**Design** / Engineering –Health –Security –Training –Education –Entertainment –E-commerce –... GATE-540 6 3D Applications/

**Analysis** **of** **Algorithms** Prof. Karen Daniels Spring, 2006 Lecture 2 Monday, 2/6/06 **Design** Patterns for Optimization Problems Greedy **Algorithms** **Algorithmic** Paradigm Context Subproblem solution order Make choice, then solve subproblem(s) Solve subproblem(s), then make choice Greedy **Algorithms** What is a Greedy **Algorithm**/ 91.503 textbook Cormen, et al. Running time? Greedy **Algorithm** ä **Algorithm**: ä S’ = presort activities in S by nondecreasing finish time ä **and** renumber ä GREEDY-ACTIVITY-SELECTOR(S’) ä n length[S’]/

Better constant approximations Online Network **Design** Demand points arrive one at a time General case as hard as online Steiner tree Tree embedding **algorithm** is online Access Network Online Special case **of** single sink **and** function Simple **algorithm**: choose cable randomly O(1/) v.s. random order inputs O(log k) v.s. adversarial order inputs Can we do better? Better **analysis**? /

**Analysis** **of** **Algorithms** Prof. Karen Daniels Fall, 2006 Lecture 2 Monday, 9/13/06 **Design** Patterns for Optimization Problems Greedy **Algorithms** **Algorithmic** Paradigm Context Subproblem solution order Make choice, then solve subproblem(s) Solve subproblem(s), then make choice Greedy **Algorithms** What is a Greedy **Algorithm**/100$120 Each item has value **and** weight. Goal: maximize total value **of** items chosen, subject to weight limit. 0-1: take all or none **of** an item fractional: can take part **of** an item source: web site /

**of** multithreaded programs (Musuvathi-Qadeer, PLDI’07) CHESS at MSR Context-bounded **analysis** for otherwise intractable systems Reachability **Analysis** **of** Multithreaded Software with Asynchronous Communication (Bouajjani-Esparza-Kiefer-Schwoon, FSTTCS’05) Context-Bounded **Analysis** **of**/**of** a context-switch (p,q) (p’,q’) Reverse stack q Reverse stack q’ 13/25 Proof (recursive case) Simulate incoming queue **and**/ the undirected underlying graph is a forest **Algorithm** 1.Reverse edges 2.Solvable using bounded context-/

AARF SampleRate –Consecutive successes/losses ARF AARF Hybrid **Algorithm** –Physical Layer metrics Hybrid **Algorithm** RBAR OAR –Long-term statistics ONOE Commercially Deployed: ARF, SampleRate **and** ONOE 6 Issues with Current **Algorithms** Current Metrics are limited in scope Simulations do not show flaws in the **algorithms** Performance loss 802.11 non-compliant **algorithms** –RBAR Flawed **design** guidelines = Flawed **algorithms** 7 Current **Design** Guidelines 1. Decrease Transmission Rate upon severe packet/

Time Domain Spectrogram Pitch **and** Formant Tracking LPC Spectra Record your own voice **and** analyze pitch **and** formants. 03/04/2005ENEE408G Spring 2005 Multimedia Signal Processing 7 Part I. Speech **Analysis** (4) 03/04/2005ENEE408G Spring 2005 Multimedia Signal Processing 8 Part I. Speech **Analysis** (5) Gender Identification: Use Auditory Toolbox to obtain Linear Predictive coefficients. **Design** your **algorithm** to identify the gender **of** samples in the training/

**of** case **analysis** Did w’ propose to m? Did m accept w’ proposal? 4simpsons.wordpress.com Questions? Extensions Fairness **of** the GS **algorithm** Different executions **of** the GS **algorithm** Main Steps in **Algorithm** **Design** Problem Statement **Algorithm** Problem Definition “Implementation” **Analysis** n! Correctness **Analysis** Definition **of** Efficiency An **algorithm**/Read Sec 1.2 **and** 2.1 in [KT] Asymptotic **Analysis** (http://xkcd.com/399/) Travelling Salesman Problem Which one is better? Now? **And** now? The actual run times n/

**algorithm** Challenge:**Design** an **algorithm** that always splits at least 50% **of** the edges Method: For each vertex, decide at random if it is red or green If fewer than half the edges are cut, repeat the experiment **Algorithm** **analysis** **Algorithm** finishes in O(m) trials w.p. 99% **Analysis**: X = number **of**/(v b )] = Pr z [ ≠ ] deterministic max-cut via “pseudorandom sources” **Analysis**: Pr[X e = 1] = Pr z [ ≠ ] let’s look at the binary strings for v a **and** v b v b = 0010101 v a = 0011001 they must differ in some position /

**Analysis** **of** **Algorithms** Prof. Karen Daniels Fall, 2008 Lecture 2 Tuesday, 9/16/08 **Design** Patterns for Optimization Problems Greedy **Algorithms** **Algorithmic** Paradigm Context Subproblem solution order Make choice, then solve subproblem(s) Solve subproblem(s), then make choice Greedy **Algorithms** What is a Greedy **Algorithm**/ 91.503 textbook Cormen, et al. Running time? Greedy **Algorithm** ä **Algorithm**: ä S’ = presort activities in S by nondecreasing finish time ä **and** renumber ä GREEDY-ACTIVITY-SELECTOR(S’) ä n length[S’]/

Time Domain Spectrogram Pitch **and** Formant Tracking LPC Spectra Record your own voice **and** analyze pitch **and** formants. 09/09/2005ENEE408G Fall 2005 Multimedia Signal Processing 7 Part I. Speech **Analysis** (4) 09/09/2005ENEE408G Fall 2005 Multimedia Signal Processing 8 Part I. Speech **Analysis** (5) Gender Identification: Use Auditory Toolbox to obtain Linear Predictive coefficients. **Design** your **algorithm** to identify the gender **of** samples in the training/

**design** – the primal-dual method 3.Network **design** – iterative rounding **and** iterative relaxation 4.Competitive **analysis** via the primal-dial method Outline 1.Basics 2.Network **design** – the primal-dual method 3.Network **design** – iterative rounding **and** iterative relaxation 4.Competitive **analysis** via the primal-dial method. What is an Approximation **Algorithm**/factor be improved? Probably not … Linear Programming Optimize a linear function over a set **of** linear constraints: minimize c ¢ x subject to: Ax ¸ 0 X ¸ 0 /

**Analysis** **and** **Design** **of** **Algorithms** An **algorithm** is a method **of** solving problem (on a computer) Problem example: –given a set **of** points on the plane –find the closest pair **Algorithm**: –find distance between all pairs Can we do it faster? Combinatorial Problems Closest pair –O(n^2) **algorithm** TSP –O(n!) **algorithm** –too slow –difficult problem Course Overview General **algorithmic** methods –divide **and** conquer, greedy **algorithms**, dynamic programming Data structures –hashing, priority queues, binary/

Lecture II : Security **Analysis** **and** Planning Internet Security: Principles & Practices John K. Zao, PhD SMIEEE National Chiao-Tung University Fall 2005 2 Internet Security - System **Analysis** & Planning Theme Objectives Highlight objectives **of** security system **design** & implementation Introduce procedure **of** security system planning & operationMotto Security/Safety is a relative measure NO system is absolutely secure ! Users’ sense **of** security is usually a fuzzy warm feeling Security specialists must /

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