# CS 188: Artificial Intelligence

Size: px
Start display at page:

Transcription

1 CS 188: Artificial Intelligence Constraint Satisfaction Problems II Instructor: Anca Dragan University of California, Berkeley Slides by Dan Klein, Pieter Abbeel, Anca Dragan (ai.berkeley.edu)

2 Today o Efficient Solution of CSPs o Local Search

3 Constraint Satisfaction Problems N variables domain D constraints x 1 x 2

4 Standard Search Formulation o Standard search formulation of CSPs o States defined by the values assigned so far (partial assignments) o Initial state: the empty assignment, {} o Successor function: assign a value to an unassigned variable o Goal test: the current assignment is complete and satisfies all constraints o We started with the straightforward, naïve approach, then improved it

5 Backtracking Search

6 Backtracking Search 1. fix ordering 2. check constraints as you go [Demo: coloring --

7 Explain it to your rubber duck! Why is it ok to fix the ordering of variables? Why is it good to fix the ordering of variables?

8 Filtering Keep track of domains for unassigned variables and cross off bad options

9 Filtering: Forward Checking o Filtering: Keep track of domains for unassigned variables and cross off bad options o Forward checking: Cross off values that violate a constraint when added to the existing assignment WA NT SA Q NSW V [Demo: coloring -- forward checking]

10 Filtering: Constraint Propagation o Forward checking propagates information from assigned to unassigned variables, but doesn't provide early detection for all failures: WA NT SA Q NSW V o NT and SA cannot both be blue! o Why didn t we detect this yet? o Constraint propagation: reason from constraint to constraint

11 Consistency of A Single Arc o An arc X Y is consistent iff for every x in the tail there is some y in the head which could be assigned without violating a constraint WA NT SA Q NSW V Delete from the tail!

12 Arc Consistency of an Entire CSP o A simple form of propagation makes sure all arcs are consistent: WA NT SA Q NSW V o Important: If X loses a value, neighbors of X need to be rechecked! o Arc consistency detects failure earlier than forward checking o Can be run as a preprocessor or after each assignment o What s the downside of enforcing arc consistency? Remember: Delete from the tail!

13 Enforcing Arc Consistency in a CSP o Runtime: O(n 2 d 3 ), can be reduced to O(n 2 d 2 ) o but detecting all possible future problems is NP-hard why?

14 Forward Checking how does it relate? o Forward checking: Cross off values that violate a constraint when added to the existing assignment WA NT SA Q NSW V [Demo: coloring -- forward checking]

15 Explain it to your rubber duck! o Forward checking is a special type of enforcing arc consistency, in which we only enforce the arcs pointing into the newly assigned variable.

16 Limitations of Arc Consistency o After enforcing arc consistency: o Can have one solution left o Can have multiple solutions left o Can have no solutions left (and not know it) o Arc consistency still runs inside a backtracking search! [Demo: coloring -- forward checking] [Demo: coloring -- arc consistency]

17 Video of Demo Coloring Backtracking with Forward Checking Complex Graph

18 Video of Demo Coloring Backtracking with Arc Consistency Complex Graph

19 K-Consistency o Increasing degrees of consistency o 1-Consistency (Node Consistency): Each single node s domain has a value which meets that node s unary constraints o 2-Consistency (Arc Consistency): For each pair of nodes, any consistent assignment to one can be extended to the other o K-Consistency: For each k nodes, any consistent assignment to k-1 can be extended to the k th node. o Higher k more expensive to compute o (You need to know the k=2 case: arc consistency)

20 Strong K-Consistency o Strong k-consistency: also k-1, k-2, 1 consistent o Claim: strong n-consistency means we can solve without backtracking! o Why? o Choose any assignment to any variable o Choose a new variable o By 2-consistency, there is a choice consistent with the first o Choose a new variable o By 3-consistency, there is a choice consistent with the first 2 o o Lots of middle ground between arc consistency and n-consistency! (e.g. k=3, called path consistency)

21 Ordering

22 Ordering: Minimum Remaining Values o Variable Ordering: Minimum remaining values (MRV): o Choose the variable with the fewest legal left values in its domain o Why min rather than max? o Also called most constrained variable o Fail-fast ordering

23 Ordering: Least Constraining Value o Value Ordering: Least Constraining Value o Given a choice of variable, choose the least constraining value o I.e., the one that rules out the fewest values in the remaining variables o Note that it may take some computation to determine this! (E.g., rerunning filtering) o Why least rather than most? o Combining these ordering ideas makes 1000 queens feasible

24 Demo: Coloring -- Backtracking + Forward Checking + Ordering

25 Summary o Work with your rubber duck to write down: o How we order variables and why o How we order values and why

26 Iterative Improvement

27 Iterative Algorithms for CSPs o Local search methods typically work with complete states, i.e., all variables assigned o To apply to CSPs: o Take an assignment with unsatisfied constraints o Operators reassign variable values o No fringe! Live on the edge. o Algorithm: While not solved, o Variable selection: randomly select any conflicted variable o Value selection: min-conflicts heuristic: o Choose a value that violates the fewest constraints o I.e., hill climb with h(x) = total number of violated constraints

28 Example: 4-Queens o States: 4 queens in 4 columns (4 4 = 256 states) o Operators: move queen in column o Goal test: no attacks o Evaluation: c(n) = number of attacks [Demo: n-queens iterative improvement (L5D1)] [Demo: coloring iterative improvement]

29 Video of Demo Iterative Improvement n Queens

30 Video of Demo Iterative Improvement Coloring

31 Local Search

32 Local Search o Tree search keeps unexplored alternatives on the fringe (ensures completeness) o Local search: improve a single option until you can t make it better (no fringe!) o New successor function: local changes o Generally much faster and more memory efficient (but incomplete and suboptimal)

33 Hill Climbing o Simple, general idea: o Start wherever o Repeat: move to the best neighboring state o If no neighbors better than current, quit o What s bad about this approach? o What s good about it?

34 Hill Climbing Diagram

35 Hill Climbing Quiz Starting from X, where do you end up? Starting from Y, where do you end up? Starting from Z, where do you end up?

36 Simulated Annealing o Idea: Escape local maxima by allowing downhill moves o But make them rarer as time goes on 38

37 Simulated Annealing o Theoretical guarantee: o Stationary distribution: o If T decreased slowly enough, will converge to optimal state! o Is this an interesting guarantee? o Sounds like magic, but reality is reality: o The more downhill steps you need to escape a local optimum, the less likely you are to ever make them all in a row o People think hard about ridge operators which let you jump around the space in better ways

38 Genetic Algorithms o Genetic algorithms use a natural selection metaphor o Keep best N hypotheses at each step (selection) based on a fitness function o Also have pairwise crossover operators, with optional mutation to give variety o Possibly the most misunderstood, misapplied (and even maligned) technique around

39 Example: N-Queens o Why does crossover make sense here? o When wouldn t it make sense? o What would mutation be? o What would a good fitness function be?

40 Bonus (time permitting): Structure

41 Problem Structure o Extreme case: independent subproblems o Example: Tasmania and mainland do not interact o Independent subproblems are identifiable as connected components of constraint graph o Suppose a graph of n variables can be broken into subproblems of only c variables: o Worst-case solution cost is O((n/c)(d c )), linear in n o E.g., n = 80, d = 2, c =20 o 2 80 = 4 billion years at 10 million nodes/sec o (4)(2 20 ) = 0.4 seconds at 10 million nodes/sec

42 Tree-Structured CSPs o Theorem: if the constraint graph has no loops, the CSP can be solved in O(n d 2 ) time o Compare to general CSPs, where worst-case time is O(d n ) o This property also applies to probabilistic reasoning (later): an example of the relation between syntactic restrictions and the complexity of reasoning

43 Tree-Structured CSPs o Algorithm for tree-structured CSPs: o Order: Choose a root variable, order variables so that parents precede children o Remove backward: For i = n : 2, apply RemoveInconsistent(Parent(X i ),X i ) o Assign forward: For i = 1 : n, assign X i consistently with Parent(X i ) o Runtime: O(n d 2 ) (why?)

44 Tree-Structured CSPs o Claim 1: After backward pass, all root-to-leaf arcs are consistent o Proof: Each X Y was made consistent at one point and Y s domain could not have been reduced thereafter (because Y s children were processed before Y) o Claim 2: If root-to-leaf arcs are consistent, forward assignment will not backtrack o Proof: Induction on position o Why doesn t this algorithm work with cycles in the constraint graph? o Note: we ll see this basic idea again with Bayes nets

45 Improving Structure

46 Nearly Tree-Structured CSPs o Conditioning: instantiate a variable, prune its neighbors' domains o Cutset conditioning: instantiate (in all ways) a set of variables such that the remaining constraint graph is a tree o Cutset size c gives runtime O( (d c ) (n-c) d 2 ), very fast for small c

47 Cutset Conditioning Choose a cutset SA Instantiate the cutset (all possible ways) SA SA SA Compute residual CSP for each assignment Solve the residual CSPs (tree structured)

48 Tree Decomposition* Idea: create a tree-structured graph of mega-variables Each mega-variable encodes part of the original CSP Subproblems overlap to ensure consistent solutions M1 M2 M3 M4 WA ¹ NT ¹ ¹ SA Agree on shared vars NT ¹ Q ¹ ¹ SA Agree on shared vars Q ¹ NS W ¹ ¹ SA Agree on shared vars NS W ¹ V ¹ ¹ SA {(WA=r,SA=g,NT=b), (WA=b,SA=r,NT=g), } {(NT=r,SA=g,Q=b), (NT=b,SA=g,Q=r), } Agree: (M1,M2) Î {((WA=g,SA=g,NT=g), (NT=g,SA=g,Q=g)), }

49 Next Time: Search when you re not the only agent!

### Smart Graphics: Methoden 3 Suche, Constraints

Smart Graphics: Methoden 3 Suche, Constraints Vorlesung Smart Graphics LMU München Medieninformatik Butz/Boring Smart Graphics SS2007 Methoden: Suche 2 Folie 1 Themen heute Suchverfahren Hillclimbing Simulated

### Y. Xiang, Constraint Satisfaction Problems

Constraint Satisfaction Problems Objectives Constraint satisfaction problems Backtracking Iterative improvement Constraint propagation Reference Russell & Norvig: Chapter 5. 1 Constraints Constraints are

### Problems in Artificial Intelligence

Problems in Artificial Intelligence Constraint Satisfaction Problems Florent Madelaine f.r.madelaine@dur.ac.uk Office in the first floor of CS building Florent Madelaine Problems in AI Durham University

### Guessing Game: NP-Complete?

Guessing Game: NP-Complete? 1. LONGEST-PATH: Given a graph G = (V, E), does there exists a simple path of length at least k edges? YES 2. SHORTEST-PATH: Given a graph G = (V, E), does there exists a simple

### CS91.543 MidTerm Exam 4/1/2004 Name: KEY. Page Max Score 1 18 2 11 3 30 4 15 5 45 6 20 Total 139

CS91.543 MidTerm Exam 4/1/2004 Name: KEY Page Max Score 1 18 2 11 3 30 4 15 5 45 6 20 Total 139 % INTRODUCTION, AI HISTORY AND AGENTS 1. [4 pts. ea.] Briefly describe the following important AI programs.

### Approximation Algorithms

Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NP-Completeness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms

### Scheduling Home Health Care with Separating Benders Cuts in Decision Diagrams

Scheduling Home Health Care with Separating Benders Cuts in Decision Diagrams André Ciré University of Toronto John Hooker Carnegie Mellon University INFORMS 2014 Home Health Care Home health care delivery

### Integer Programming: Algorithms - 3

Week 9 Integer Programming: Algorithms - 3 OPR 992 Applied Mathematical Programming OPR 992 - Applied Mathematical Programming - p. 1/12 Dantzig-Wolfe Reformulation Example Strength of the Linear Programming

### Satisfiability Checking

Satisfiability Checking SAT-Solving Prof. Dr. Erika Ábrahám Theory of Hybrid Systems Informatik 2 WS 10/11 Prof. Dr. Erika Ábrahám - Satisfiability Checking 1 / 40 A basic SAT algorithm Assume the CNF

### 5.1 Bipartite Matching

CS787: Advanced Algorithms Lecture 5: Applications of Network Flow In the last lecture, we looked at the problem of finding the maximum flow in a graph, and how it can be efficiently solved using the Ford-Fulkerson

### Scheduling Shop Scheduling. Tim Nieberg

Scheduling Shop Scheduling Tim Nieberg Shop models: General Introduction Remark: Consider non preemptive problems with regular objectives Notation Shop Problems: m machines, n jobs 1,..., n operations

### Search methods motivation 1

Suppose you are an independent software developer, and your software package Windows Defeater R, widely available on sourceforge under a GNU GPL license, is getting an international attention and acclaim.

### Genetic Algorithms and Sudoku

Genetic Algorithms and Sudoku Dr. John M. Weiss Department of Mathematics and Computer Science South Dakota School of Mines and Technology (SDSM&T) Rapid City, SD 57701-3995 john.weiss@sdsmt.edu MICS 2009

### A Constraint Programming based Column Generation Approach to Nurse Rostering Problems

Abstract A Constraint Programming based Column Generation Approach to Nurse Rostering Problems Fang He and Rong Qu The Automated Scheduling, Optimisation and Planning (ASAP) Group School of Computer Science,

### Lecture. Simulation and optimization

Course Simulation Lecture Simulation and optimization 1 4/3/2015 Simulation and optimization Platform busses at Schiphol Optimization: Find a feasible assignment of bus trips to bus shifts (driver and

### ! Solve problem to optimality. ! Solve problem in poly-time. ! Solve arbitrary instances of the problem. #-approximation algorithm.

Approximation Algorithms 11 Approximation Algorithms Q Suppose I need to solve an NP-hard problem What should I do? A Theory says you're unlikely to find a poly-time algorithm Must sacrifice one of three

### Applied Algorithm Design Lecture 5

Applied Algorithm Design Lecture 5 Pietro Michiardi Eurecom Pietro Michiardi (Eurecom) Applied Algorithm Design Lecture 5 1 / 86 Approximation Algorithms Pietro Michiardi (Eurecom) Applied Algorithm Design

### ! Solve problem to optimality. ! Solve problem in poly-time. ! Solve arbitrary instances of the problem. !-approximation algorithm.

Approximation Algorithms Chapter Approximation Algorithms Q Suppose I need to solve an NP-hard problem What should I do? A Theory says you're unlikely to find a poly-time algorithm Must sacrifice one of

### Binary Heaps * * * * * * * / / \ / \ / \ / \ / \ * * * * * * * * * * * / / \ / \ / / \ / \ * * * * * * * * * *

Binary Heaps A binary heap is another data structure. It implements a priority queue. Priority Queue has the following operations: isempty add (with priority) remove (highest priority) peek (at highest

CSE / Notes : Task Scheduling & Load Balancing Task Scheduling A task is a (sequential) activity that uses a set of inputs to produce a set of outputs. A task (precedence) graph is an acyclic, directed

Load Balancing Backtracking, branch & bound and alpha-beta pruning: how to assign work to idle processes without much communication? Additionally for alpha-beta pruning: implementing the young-brothers-wait

### A binary heap is a complete binary tree, where each node has a higher priority than its children. This is called heap-order property

CmSc 250 Intro to Algorithms Chapter 6. Transform and Conquer Binary Heaps 1. Definition A binary heap is a complete binary tree, where each node has a higher priority than its children. This is called

### The Problem of Scheduling Technicians and Interventions in a Telecommunications Company

The Problem of Scheduling Technicians and Interventions in a Telecommunications Company Sérgio Garcia Panzo Dongala November 2008 Abstract In 2007 the challenge organized by the French Society of Operational

### CS473 - Algorithms I

CS473 - Algorithms I Lecture 9 Sorting in Linear Time View in slide-show mode 1 How Fast Can We Sort? The algorithms we have seen so far: Based on comparison of elements We only care about the relative

### CS104: Data Structures and Object-Oriented Design (Fall 2013) October 24, 2013: Priority Queues Scribes: CS 104 Teaching Team

CS104: Data Structures and Object-Oriented Design (Fall 2013) October 24, 2013: Priority Queues Scribes: CS 104 Teaching Team Lecture Summary In this lecture, we learned about the ADT Priority Queue. A

### INTEGER PROGRAMMING. Integer Programming. Prototype example. BIP model. BIP models

Integer Programming INTEGER PROGRAMMING In many problems the decision variables must have integer values. Example: assign people, machines, and vehicles to activities in integer quantities. If this is

### Integrating Benders decomposition within Constraint Programming

Integrating Benders decomposition within Constraint Programming Hadrien Cambazard, Narendra Jussien email: {hcambaza,jussien}@emn.fr École des Mines de Nantes, LINA CNRS FRE 2729 4 rue Alfred Kastler BP

### each college c i C has a capacity q i - the maximum number of students it will admit

n colleges in a set C, m applicants in a set A, where m is much larger than n. each college c i C has a capacity q i - the maximum number of students it will admit each college c i has a strict order i

### University of Potsdam Faculty of Computer Science. Clause Learning in SAT Seminar Automatic Problem Solving WS 2005/06

University of Potsdam Faculty of Computer Science Clause Learning in SAT Seminar Automatic Problem Solving WS 2005/06 Authors: Richard Tichy, Thomas Glase Date: 25th April 2006 Contents 1 Introduction

### Dynamic Programming. Lecture 11. 11.1 Overview. 11.2 Introduction

Lecture 11 Dynamic Programming 11.1 Overview Dynamic Programming is a powerful technique that allows one to solve many different types of problems in time O(n 2 ) or O(n 3 ) for which a naive approach

### Genetic Algorithm. Based on Darwinian Paradigm. Intrinsically a robust search and optimization mechanism. Conceptual Algorithm

24 Genetic Algorithm Based on Darwinian Paradigm Reproduction Competition Survive Selection Intrinsically a robust search and optimization mechanism Slide -47 - Conceptual Algorithm Slide -48 - 25 Genetic

### From Last Time: Remove (Delete) Operation

CSE 32 Lecture : More on Search Trees Today s Topics: Lazy Operations Run Time Analysis of Binary Search Tree Operations Balanced Search Trees AVL Trees and Rotations Covered in Chapter of the text From

### NP-complete? NP-hard? Some Foundations of Complexity. Prof. Sven Hartmann Clausthal University of Technology Department of Informatics

NP-complete? NP-hard? Some Foundations of Complexity Prof. Sven Hartmann Clausthal University of Technology Department of Informatics Tractability of Problems Some problems are undecidable: no computer

### Dynamic programming formulation

1.24 Lecture 14 Dynamic programming: Job scheduling Dynamic programming formulation To formulate a problem as a dynamic program: Sort by a criterion that will allow infeasible combinations to be eli minated

### A* Algorithm Based Optimization for Cloud Storage

International Journal of Digital Content Technology and its Applications Volume 4, Number 8, November 21 A* Algorithm Based Optimization for Cloud Storage 1 Ren Xun-Yi, 2 Ma Xiao-Dong 1* College of Computer

### Graphing Parabolas With Microsoft Excel

Graphing Parabolas With Microsoft Excel Mr. Clausen Algebra 2 California State Standard for Algebra 2 #10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

### Fairness in Routing and Load Balancing

Fairness in Routing and Load Balancing Jon Kleinberg Yuval Rabani Éva Tardos Abstract We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria

### A Constraint-Based Method for Project Scheduling with Time Windows

A Constraint-Based Method for Project Scheduling with Time Windows Amedeo Cesta 1 and Angelo Oddi 1 and Stephen F. Smith 2 1 ISTC-CNR, National Research Council of Italy Viale Marx 15, I-00137 Rome, Italy,

### CMPSCI611: Approximating MAX-CUT Lecture 20

CMPSCI611: Approximating MAX-CUT Lecture 20 For the next two lectures we ll be seeing examples of approximation algorithms for interesting NP-hard problems. Today we consider MAX-CUT, which we proved to

### Full and Complete Binary Trees

Full and Complete Binary Trees Binary Tree Theorems 1 Here are two important types of binary trees. Note that the definitions, while similar, are logically independent. Definition: a binary tree T is full

### SYSM 6304: Risk and Decision Analysis Lecture 5: Methods of Risk Analysis

SYSM 6304: Risk and Decision Analysis Lecture 5: Methods of Risk Analysis M. Vidyasagar Cecil & Ida Green Chair The University of Texas at Dallas Email: M.Vidyasagar@utdallas.edu October 17, 2015 Outline

### Binary Encodings of Non-binary Constraint Satisfaction Problems: Algorithms and Experimental Results

Journal of Artificial Intelligence Research 24 (2005) 641-684 Submitted 04/05; published 11/05 Binary Encodings of Non-binary Constraint Satisfaction Problems: Algorithms and Experimental Results Nikolaos

### Binary Search Trees. Data in each node. Larger than the data in its left child Smaller than the data in its right child

Binary Search Trees Data in each node Larger than the data in its left child Smaller than the data in its right child FIGURE 11-6 Arbitrary binary tree FIGURE 11-7 Binary search tree Data Structures Using

### Single machine models: Maximum Lateness -12- Approximation ratio for EDD for problem 1 r j,d j < 0 L max. structure of a schedule Q...

Lecture 4 Scheduling 1 Single machine models: Maximum Lateness -12- Approximation ratio for EDD for problem 1 r j,d j < 0 L max structure of a schedule 0 Q 1100 11 00 11 000 111 0 0 1 1 00 11 00 11 00

### Constraint Programming for the Vehicle Routing Problem. Philip Kilby

Constraint Programming for the Vehicle Routing Problem Philip Kilby A bit about NICTA National Information and Communications Technology Australia (NICTA) Research in ICT since 24 Major Labs in Sydney,

### Lecture 3. Linear Programming. 3B1B Optimization Michaelmas 2015 A. Zisserman. Extreme solutions. Simplex method. Interior point method

Lecture 3 3B1B Optimization Michaelmas 2015 A. Zisserman Linear Programming Extreme solutions Simplex method Interior point method Integer programming and relaxation The Optimization Tree Linear Programming

### Measuring the Performance of an Agent

25 Measuring the Performance of an Agent The rational agent that we are aiming at should be successful in the task it is performing To assess the success we need to have a performance measure What is rational

### Inteligencia Artificial Representación del conocimiento a través de restricciones (continuación)

Inteligencia Artificial Representación del conocimiento a través de restricciones (continuación) Gloria Inés Alvarez V. Pontifica Universidad Javeriana Cali Periodo 2014-2 Material de David L. Poole and

### Network Flow I. Lecture 16. 16.1 Overview. 16.2 The Network Flow Problem

Lecture 6 Network Flow I 6. Overview In these next two lectures we are going to talk about an important algorithmic problem called the Network Flow Problem. Network flow is important because it can be

### 2. (a) Explain the strassen s matrix multiplication. (b) Write deletion algorithm, of Binary search tree. [8+8]

Code No: R05220502 Set No. 1 1. (a) Describe the performance analysis in detail. (b) Show that f 1 (n)+f 2 (n) = 0(max(g 1 (n), g 2 (n)) where f 1 (n) = 0(g 1 (n)) and f 2 (n) = 0(g 2 (n)). [8+8] 2. (a)

### CHAPTER 3 SECURITY CONSTRAINED OPTIMAL SHORT-TERM HYDROTHERMAL SCHEDULING

60 CHAPTER 3 SECURITY CONSTRAINED OPTIMAL SHORT-TERM HYDROTHERMAL SCHEDULING 3.1 INTRODUCTION Optimal short-term hydrothermal scheduling of power systems aims at determining optimal hydro and thermal generations

### NP-Completeness I. Lecture 19. 19.1 Overview. 19.2 Introduction: Reduction and Expressiveness

Lecture 19 NP-Completeness I 19.1 Overview In the past few lectures we have looked at increasingly more expressive problems that we were able to solve using efficient algorithms. In this lecture we introduce

### Outline. NP-completeness. When is a problem easy? When is a problem hard? Today. Euler Circuits

Outline NP-completeness Examples of Easy vs. Hard problems Euler circuit vs. Hamiltonian circuit Shortest Path vs. Longest Path 2-pairs sum vs. general Subset Sum Reducing one problem to another Clique

### Design of LDPC codes

Design of LDPC codes Codes from finite geometries Random codes: Determine the connections of the bipartite Tanner graph by using a (pseudo)random algorithm observing the degree distribution of the code

### Evaluation of Different Task Scheduling Policies in Multi-Core Systems with Reconfigurable Hardware

Evaluation of Different Task Scheduling Policies in Multi-Core Systems with Reconfigurable Hardware Mahyar Shahsavari, Zaid Al-Ars, Koen Bertels,1, Computer Engineering Group, Software & Computer Technology

### A Review And Evaluations Of Shortest Path Algorithms

A Review And Evaluations Of Shortest Path Algorithms Kairanbay Magzhan, Hajar Mat Jani Abstract: Nowadays, in computer networks, the routing is based on the shortest path problem. This will help in minimizing

### M. Sugumaran / (IJCSIT) International Journal of Computer Science and Information Technologies, Vol. 2 (3), 2011, 1001-1006

A Design of Centralized Meeting Scheduler with Distance Metrics M. Sugumaran Department of Computer Science and Engineering,Pondicherry Engineering College, Puducherry, India. Abstract Meeting scheduling

### Minimum cost maximum flow, Minimum cost circulation, Cost/Capacity scaling

6.854 Advanced Algorithms Lecture 16: 10/11/2006 Lecturer: David Karger Scribe: Kermin Fleming and Chris Crutchfield, based on notes by Wendy Chu and Tudor Leu Minimum cost maximum flow, Minimum cost circulation,

### Introduction & Overview

ID2204: Constraint Programming Introduction & Overview Lecture 01, Christian Schulte cschulte@kth.se Software and Computer Systems School of Information and Communication Technology KTH Royal Institute

### Game Theory 1. Introduction

Game Theory 1. Introduction Dmitry Potapov CERN What is Game Theory? Game theory is about interactions among agents that are self-interested I ll use agent and player synonymously Self-interested: Each

### Circuits 1 M H Miller

Introduction to Graph Theory Introduction These notes are primarily a digression to provide general background remarks. The subject is an efficient procedure for the determination of voltages and currents

### A Computer Application for Scheduling in MS Project

Comput. Sci. Appl. Volume 1, Number 5, 2014, pp. 309-318 Received: July 18, 2014; Published: November 25, 2014 Computer Science and Applications www.ethanpublishing.com Anabela Tereso, André Guedes and

### APPLICATION OF ADVANCED SEARCH- METHODS FOR AUTOMOTIVE DATA-BUS SYSTEM SIGNAL INTEGRITY OPTIMIZATION

APPLICATION OF ADVANCED SEARCH- METHODS FOR AUTOMOTIVE DATA-BUS SYSTEM SIGNAL INTEGRITY OPTIMIZATION Harald Günther 1, Stephan Frei 1, Thomas Wenzel, Wolfgang Mickisch 1 Technische Universität Dortmund,

### Software that writes Software Stochastic, Evolutionary, MultiRun Strategy Auto-Generation. TRADING SYSTEM LAB Product Description Version 1.

Software that writes Software Stochastic, Evolutionary, MultiRun Strategy Auto-Generation TRADING SYSTEM LAB Product Description Version 1.1 08/08/10 Trading System Lab (TSL) will automatically generate

### CS 2112 Spring 2014. 0 Instructions. Assignment 3 Data Structures and Web Filtering. 0.1 Grading. 0.2 Partners. 0.3 Restrictions

CS 2112 Spring 2014 Assignment 3 Data Structures and Web Filtering Due: March 4, 2014 11:59 PM Implementing spam blacklists and web filters requires matching candidate domain names and URLs very rapidly

### The Goldberg Rao Algorithm for the Maximum Flow Problem

The Goldberg Rao Algorithm for the Maximum Flow Problem COS 528 class notes October 18, 2006 Scribe: Dávid Papp Main idea: use of the blocking flow paradigm to achieve essentially O(min{m 2/3, n 1/2 }

### Local Search and Constraint Programming for the Post Enrolment-based Course Timetabling Problem

Local Search and Constraint Programming for the Post Enrolment-based Course Timetabling Problem Hadrien Cambazard, Emmanuel Hebrard, Barry O Sullivan and Alexandre Papadopoulos Cork Constraint Computation

### Keywords: Power Transmission Networks, Maintenance Scheduling problem, Hybrid Constraint Methods, Constraint Programming

SCHEDULING MAINTENANCE ACTIVITIES OF ELECTRIC POWER TRANSMISSION NETWORKS USING AN HYBRID CONSTRAINT METHOD Nuno Gomes, Raul Pinheiro, ZitaVale, Carlos Ramos GECAD Knowledge Engineering and Decision Support

### A Branch and Bound Algorithm for Solving the Binary Bi-level Linear Programming Problem

A Branch and Bound Algorithm for Solving the Binary Bi-level Linear Programming Problem John Karlof and Peter Hocking Mathematics and Statistics Department University of North Carolina Wilmington Wilmington,

### STUDY OF PROJECT SCHEDULING AND RESOURCE ALLOCATION USING ANT COLONY OPTIMIZATION 1

STUDY OF PROJECT SCHEDULING AND RESOURCE ALLOCATION USING ANT COLONY OPTIMIZATION 1 Prajakta Joglekar, 2 Pallavi Jaiswal, 3 Vandana Jagtap Maharashtra Institute of Technology, Pune Email: 1 somanprajakta@gmail.com,

### Today s topic: So far, we have talked about. Question. Task models

Overall Stucture of Real Time Systems So far, we have talked about Task...... Task n Programming Languages to implement the Tasks Run-TIme/Operating Systems to run the Tasks RTOS/Run-Time System Hardware

### The Union-Find Problem Kruskal s algorithm for finding an MST presented us with a problem in data-structure design. As we looked at each edge,

The Union-Find Problem Kruskal s algorithm for finding an MST presented us with a problem in data-structure design. As we looked at each edge, cheapest first, we had to determine whether its two endpoints

### The Minimum Consistent Subset Cover Problem and its Applications in Data Mining

The Minimum Consistent Subset Cover Problem and its Applications in Data Mining Byron J Gao 1,2, Martin Ester 1, Jin-Yi Cai 2, Oliver Schulte 1, and Hui Xiong 3 1 School of Computing Science, Simon Fraser

### Machine Learning for Naive Bayesian Spam Filter Tokenization

Machine Learning for Naive Bayesian Spam Filter Tokenization Michael Bevilacqua-Linn December 20, 2003 Abstract Background Traditional client level spam filters rely on rule based heuristics. While these

### Course: Model, Learning, and Inference: Lecture 5

Course: Model, Learning, and Inference: Lecture 5 Alan Yuille Department of Statistics, UCLA Los Angeles, CA 90095 yuille@stat.ucla.edu Abstract Probability distributions on structured representation.

### Practical Guide to the Simplex Method of Linear Programming

Practical Guide to the Simplex Method of Linear Programming Marcel Oliver Revised: April, 0 The basic steps of the simplex algorithm Step : Write the linear programming problem in standard form Linear

### A search based Sudoku solver

A search based Sudoku solver Tristan Cazenave Labo IA Dept. Informatique Université Paris 8, 93526, Saint-Denis, France, cazenave@ai.univ-paris8.fr Abstract. Sudoku is a popular puzzle. In this paper we

### Analysis of Algorithms I: Binary Search Trees

Analysis of Algorithms I: Binary Search Trees Xi Chen Columbia University Hash table: A data structure that maintains a subset of keys from a universe set U = {0, 1,..., p 1} and supports all three dictionary

### A hybrid approach for solving real-world nurse rostering problems

Presentation at CP 2011: A hybrid approach for solving real-world nurse rostering problems Martin Stølevik (martin.stolevik@sintef.no) Tomas Eric Nordlander (tomas.nordlander@sintef.no) Atle Riise (atle.riise@sintef.no)

### A Reactive Tabu Search for Service Restoration in Electric Power Distribution Systems

IEEE International Conference on Evolutionary Computation May 4-11 1998, Anchorage, Alaska A Reactive Tabu Search for Service Restoration in Electric Power Distribution Systems Sakae Toune, Hiroyuki Fudo,

### Agent-based decentralised coordination for sensor networks using the max-sum algorithm

DOI 10.1007/s10458-013-9225-1 Agent-based decentralised coordination for sensor networks using the max-sum algorithm A. Farinelli A. Rogers N. R. Jennings The Author(s) 2013 Abstract In this paper, we

### CIS 631 Database Management Systems Sample Final Exam

CIS 631 Database Management Systems Sample Final Exam 1. (25 points) Match the items from the left column with those in the right and place the letters in the empty slots. k 1. Single-level index files

### Genetic Algorithm Based Interconnection Network Topology Optimization Analysis

Genetic Algorithm Based Interconnection Network Topology Optimization Analysis 1 WANG Peng, 2 Wang XueFei, 3 Wu YaMing 1,3 College of Information Engineering, Suihua University, Suihua Heilongjiang, 152061

### Integration of ACO in a Constraint Programming Language

Integration of ACO in a Constraint Programming Language Madjid Khichane 12, Patrick Albert 1, and Christine Solnon 2 1 ILOG 2 LIRIS, UMR 5205 CNRS / University of Lyon ANTS 08 Motivations Ant Colony Optimization

### Binary Search Trees. A Generic Tree. Binary Trees. Nodes in a binary search tree ( B-S-T) are of the form. P parent. Key. Satellite data L R

Binary Search Trees A Generic Tree Nodes in a binary search tree ( B-S-T) are of the form P parent Key A Satellite data L R B C D E F G H I J The B-S-T has a root node which is the only node whose parent

### Data Structures. Algorithm Performance and Big O Analysis

Data Structures Algorithm Performance and Big O Analysis What s an Algorithm? a clearly specified set of instructions to be followed to solve a problem. In essence: A computer program. In detail: Defined

### Compact Representations and Approximations for Compuation in Games

Compact Representations and Approximations for Compuation in Games Kevin Swersky April 23, 2008 Abstract Compact representations have recently been developed as a way of both encoding the strategic interactions

### A Systematic Approach to Model-Guided Empirical Search for Memory Hierarchy Optimization

A Systematic Approach to Model-Guided Empirical Search for Memory Hierarchy Optimization Chun Chen, Jacqueline Chame, Mary Hall, and Kristina Lerman University of Southern California/Information Sciences

### Compression algorithm for Bayesian network modeling of binary systems

Compression algorithm for Bayesian network modeling of binary systems I. Tien & A. Der Kiureghian University of California, Berkeley ABSTRACT: A Bayesian network (BN) is a useful tool for analyzing the

### Optimized Software Component Allocation On Clustered Application Servers. by Hsiauh-Tsyr Clara Chang, B.B., M.S., M.S.

Optimized Software Component Allocation On Clustered Application Servers by Hsiauh-Tsyr Clara Chang, B.B., M.S., M.S. Submitted in partial fulfillment of the requirements for the degree of Doctor of Professional

Approximation Algorithms Chapter Approximation Algorithms Q. Suppose I need to solve an NP-hard problem. What should I do? A. Theory says you're unlikely to find a poly-time algorithm. Must sacrifice one

### Lecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs

CSE599s: Extremal Combinatorics November 21, 2011 Lecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs Lecturer: Anup Rao 1 An Arithmetic Circuit Lower Bound An arithmetic circuit is just like

### Introduction to Logic in Computer Science: Autumn 2006

Introduction to Logic in Computer Science: Autumn 2006 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 Plan for Today Now that we have a basic understanding

### Testing LTL Formula Translation into Büchi Automata

Testing LTL Formula Translation into Büchi Automata Heikki Tauriainen and Keijo Heljanko Helsinki University of Technology, Laboratory for Theoretical Computer Science, P. O. Box 5400, FIN-02015 HUT, Finland

### Max Flow, Min Cut, and Matchings (Solution)

Max Flow, Min Cut, and Matchings (Solution) 1. The figure below shows a flow network on which an s-t flow is shown. The capacity of each edge appears as a label next to the edge, and the numbers in boxes

### Introduction Solvability Rules Computer Solution Implementation. Connect Four. March 9, 2010. Connect Four

March 9, 2010 is a tic-tac-toe like game in which two players drop discs into a 7x6 board. The first player to get four in a row (either vertically, horizontally, or diagonally) wins. The game was first

### Automatic Configuration Generation for Service High Availability with Load Balancing

Automatic Configuration Generation for Service High Availability with Load Balancing A. Kanso 1, F. Khendek 1, M. Toeroe 2, A. Hamou-Lhadj 1 1 Electrical and Computer Engineering Department, Concordia

### Constraint Optimization for Highly Constrained Logistic Problems

Constraint Optimization for Highly Constrained Logistic Problems Maria Kinga Mochnacs Meang Akira Tanaka Anders Nyborg Rune Møller Jensen IT University Technical Report Series TR-2007-2008-104 ISSN 1600