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Course Number: CS 5420, Fall 2009

College/University: FIU

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FIU - CS - 5420
1P = IW?ACEADISHAMIRInstitute of Science, Reholot, IsraelThe WelzrnannAbstract. In this paper, it is proven that when both randomization and interaction are allowed, the proofs that can be verified in polynomial time are exactly those proofs
FIU - CS - 5420
1P = PSPACE:SimplifiedProofA.SHENof Sciences, Moscow, Rassia, CISAcademyAbstract, Lund et al. [1] have proved that PH is contained in 1P. Shamir [2] improved this technique and proved that PSPACE = 1P. In this note, a slightly simphfied
FIU - CS - 5420
A Quantitative Comparison of Parallel Computation ModelsBEN H. H. JUURLINK Delft University of Technology and HARRY A. G. WIJSHOFF Leiden UniversityIn recent years, a large number of parallel computation models have been proposed to replace the PR
FIU - CS - 5420
AlgebraicMethodsfor InteractiveProof SystemsCARSTENUnu>ersityLUND,LANCEChicago,FORTNOW,ANDHOWARDKARLOFFof Clucago,Il[moisAND NOAMHebrewNISANUnuemi@ Jen{salern, IsraelAbstract. A new algebraic technique for the constr
FIU - CS - 5420
CDMTCS Research Report Series Computing with Membranes: P Systems with Worm-ObjectsJuan Castellanos Department of Artificial Intelligence, Faculty of Computer Science, Politechnical University of Madrid Gheorghe Pun a Institute of Mathematics of the
FIU - CS - 5420
%!PS-Adobe-3.0 %Title: 30092 %Creator: DVIPSONE 1.1.3 1994 Mar 19 11:55:59 SN 314 %CreationDate: 1997 Sep 03 12:11:18 %BoundingBox: 72 88 441 720 %Pages: 63 %PageOrder: Ascend %DocumentSuppliedResources: font cmbx10 cmsy7 cmr8 cmsy6 cmr7 cmr6 cmr5 %+
FIU - CS - 5420
4 W Y bDeyu $ 9f9 i u 7 7 4 6 q)('X5wf0bD eyYhe #IIyGXWCy IbXW U ayy(yeX'x& 7 w u % c 7 7 s r 6 6 4 vt&IfY@$C9teu'5 q i % 7 % 7 g P 4 H e P Q II4
San Diego State - ART - 448
Yuki Kusuhara ART348: 3D Digital Design 3/15/09Design Brief: Type Monument "ROLL"1. Your definition and description of the problems The Problem for this design is to decide which appropriate background to go with an appropriate text. Also how to c
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 1; Due January 24 in class.]Problem DescriptionYou have been given a regular deck of 52 cards. At the start, the deck of cards is in perfect increasing order, i.e., the deck when placed
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 1; Due January 24 in class.]Problem DescriptionYou have been given a regular deck of 52 cards. At the start, the deck of cards is in perfect increasing order, i.e., the deck when placed
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 1; Due January 24 in class.]Problem DescriptionYou have been given a regular deck of 52 cards. At the start, the deck of cards is in perfect increasing order, i.e., the deck when placed
FIU - CS - 3530
/* File: Deck.java */package cop3530;import java.util.Comparator;public interface Deck{ public void perfectShuffle(); public int locateSpecial(); public Object findMax( Object [] a, int startIndex, int incrIndex, Comparator cmp
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 2; Due February 14 in class.]Traveling Salesperson Heuristics Problem DescriptionYour task is to write a program to compute an approximate solution to the traveling salesperson problem.
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 2; Due February 14 in class.]Traveling Salesperson Heuristics Problem DescriptionYour task is to write a program to compute an approximate solution to the traveling salesperson problem.
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 3; Due March 7 in my office.]Recursion Problem DescriptionYour task is to write a recursive program to draw "fractal images" such as Tree.ps, which is shown on the course web page. Your
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 3; Due April 9 in my office.]Hashing Problem DescriptionYour task is to write a program to read the first Act of Shakespeare's play Hamlet and create a hash table of all the words in th
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 5; Due April 18 in my office.]Shortest Paths Problem DescriptionYour task is to write a program to use Dijkstra's algorithm to compute the shortest paths between two cities. In the firs
FIU - CS - 3530
SPRING 2002: COP 3530 Data Structures[Programming Assignment 5; Due April 18 in my office.]Shortest Paths Problem DescriptionYour task is to write a program to use Dijkstra's algorithm to compute the shortest paths between two cities. In the firs
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework Guidelines and Collaboration Policies] General submission guidelines: Since people tend to scribble on handwritten homework, you are required to type up your assignment and print it out. Problems are
FIU - CS - 5407
COT 5407: Introduction to AlgorithmsGiri NarasimhanECS 254A; Phone: x3748 giri@cis.fiu.eduhttp:/www.cis.fiu.edu/~giri/teach/5407F08.htmlhttps:/online.cis.fiu.edu/portal/course/view.php?id=2858/28/07 COT 5407 1Algorithms are "recipes"!8/28/0
FIU - CS - 5407
Evaluation Exams (2) Quizzes Homework Assignments Semester Project Class Participation 50% 10% 30% 5% 5%http:/www.cis.fiu.edu/~giri/teach/5407F08.htmlhttps:/online.cis.fiu.edu/portal/course/view.php?id=2859/4/08COT 54071DefinitionsAl
FIU - CS - 5407
Exam Dates (Tentative) Midterm Final Exam Homework Assignments Sep 11, Sep 23, Oct 2, Oct 14, Oct 23, Nov 4, Nov 18October 9 December 11 (?) Quizzes Sep 23, Oct 2, Oct 14, Oct 23, Nov 4, Nov 18, Semester ProjectOctober 19/9/08COT 540
FIU - CS - 5407
Animation Demos http:/cg.scs.carleton.ca/~morin/misc/sortalg/ http:/home.westman.wave.ca/~rhenry/sort/ Shows time complexities on best, worst and average case http:/vision.bc.edu/~dmartin/teaching/sorting/animhtml/quick3.html runs on almost sor
FIU - CS - 5407
Animation Demos http:/cg.scs.carleton.ca/~morin/misc/sortalg/ http:/home.westman.wave.ca/~rhenry/sort/ Shows time complexities on best, worst and average case http:/vision.bc.edu/~dmartin/teaching/sorting/animhtml/quick3.html runs on almost sor
FIU - CS - 5407
Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9/18/08COT 54071Show: f(n) = O(g(n) & f(n) To show f(n) = O(g(n)O(g(n) Manipulate g(n) so that f(n) <= c g(n) for some n0. Then try to show that
FIU - CS - 5407
QuickSortPage 146, CLRS9/23/08 COT 5407 1Analysis of QuickSort Average case T(n) <= 2T(n/2) + O(n) T(n) = O(n log n) Worst case T(n) = T(n-1) + O(n) T(n) = O(n2) "IN PLACE" sorting algorithm Which sorting algorithm is not an "IN PLACE"
FIU - CS - 5407
HeapSort: Part 1O(height of node in location i) = O(log(size of subtree)p1309/25/08 COT 5407 1HeapSort: Part 2O(log n)Total: O(nlog n)9/25/08COT 54072Build-Max-Heap Analysis9/25/08COT 54073Visualizing Algorithms 1Position W
FIU - CS - 5407
Exam Dates (Tentative) Midterm Final Exam Homework Assignments Sep 11, Sep 23, Oct 2, Oct 14, Oct 23, Nov 4, Nov 18October 9 December 11 (?) Quizzes Sep 23, Oct 2, Oct 14, Oct 23, Nov 4, Nov 18, Semester ProjectOctober 19/30/08COT 54
FIU - CS - 5407
Order Statistics Maximum, Minimum 7 MinMax 2(n-1) comparisons 3n/2 comparisonsn-1 comparisons 9 4 8 2 5 0 631 Max and 2ndMax (n-1) + (n-2) comparisons ?10/2/08COT 54071k-Selection; Median Select the k-th smallest item in list
FIU - CS - 5407
Exam: Lessons to be learnt (log n)2 log (n2) If A > C and B > D, then A + B > C + D To disprove A + B > C + D it is not enough to show that A <= C or B <= D it is enough to show that A <= C and B <= D 10/9 < 5/4 because 10/9 = 40/36, while 5/
FIU - CS - 5407
BST: InsertTime Complexity: O(h) h = height of binary search treeSearch for x in TInsert x as leaf in T10/21/08COT 54071BST: DeleteTime Complexity: O(h) h = height of binary search treeSet y as the node to be deleted. It has at most on
FIU - CS - 5407
RotationsLeftRotate(T,x) / pg 278 / right child of x becomes x's parent. / Subtrees need to be readjusted. y = right[x] right[x] = left[y] p[left[y] = x p[y] = p[x] if (p[x] = NIL[T]) then root[T] = y else if (x = left[p[x]) then left[p[x] = y else
FIU - CS - 5407
RB-Tree Augmentation Augment x with Size(x), where Size(x) = size of subtree rooted at x Size(NIL) = 010/28/08COT 54071Augmented Data Structures Why is it needed? Because basic data structures not enough for all operations storing extra
FIU - CS - 5407
Greedy Algorithms Huffman Coding Huffman Coding Problem Example: Release 29.1 of 15-Feb-2005 of TrEMBL Protein Database contains 1,614,107 sequence entries, comprising 505,947,503 amino acids. There are 20 possible amino acids. What is the minimum
FIU - CS - 5407
Dynamic Programmming: Activity Selection Select the maximum number of non-overlapping activities from a set of n activities A = {a1, ., an} (sorted by finish times). Identify "easier" subproblems to solve. A1 = {a1} A2 = {a1, a2} A3 = {a1, a2, a3},
FIU - CS - 5407
Dynamic Programming vs. Divide-&-conquer Divide-&-conquer works best when all subproblems are independent. So, pick partition that makes algorithm most efficient & simply combine solutions to solve entire problem. Dynamic programming is needed when
FIU - CS - 5407
11/18/08COT 54071DFS(G) 1. 2. 3. 4. 5. 6. 7. Time For each vertex u color[u] [u] 0 V[G] do NIL DFS-VISIT(u) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. color[u] 12. F[u] V[G] do WHITEO(m+n)For each vertex uif color[u] = WHITE then DFS-VISIT(u)Vi
FIU - CS - 5407
Correctness of Dijkstra s algorithm Invariant: When vertex u is deleted from the priority queue, d[u] is the correct length of the shortest path from the source s to vertex u. Additionally, the value d[u] will never change after that iteration. P
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework 0; No Submission Required] General submission guidelines and policies: Read page 2 of this assignment. Collaboration Statement: Every homework must be accompanied by the following statement along wit
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework 1; Due Sep 23 at start of class] General submission guidelines and policies: Add the following signed statement. Without this statement, your homework will not be graded. I have adhered to the collab
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework 2; Due Oct 2 at start of class] General submission guidelines and policies: Add the following signed statement. Without this statement, your homework will not be graded. I have adhered to the collabo
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework 3; Due Oct 14 at start of class] General submission guidelines and policies: Add the following signed statement. Without this statement, your homework will not be graded. I have adhered to the collab
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework 4; Due Oct 30 at start of class] General submission guidelines and policies: Add the following signed statement. Without this statement, your homework will not be graded. I have adhered to the collab
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework 5; Due Nov 18 at start of class] General submission guidelines and policies: Add the following signed statement. Without this statement, your homework will not be graded. I have adhered to the collab
FIU - CS - 5407
FALL 2008: COT 5407 Intro. to Algorithms[Homework 6; Due Dec 2 (NOT Nov 30) at start of class] General submission guidelines and policies: Add the following signed statement. Without this statement, your homework will not be graded. I have adhered t
FIU - CS - 5407
Fall 2008: COT 5407 Intro. to Algorithms[Programming Assignment 1; Due Dec 2 at start of class] General submission guidelines and policies: Add the following signed statement. Without this statement, your homework will not be graded. I have adhered
FIU - CS - 3530
Inheritance Defines a IS-A relationship between classes. Base classes and derived classes. Derived class inherits all fields and methods of base class. Derived class objects are type compatible with base class. protected fields and methods:
FIU - CS - 3530
Wrappers and Adapters A wrapper class stores an entity and adds operations that the original type did not support correctly. Java has wrapper types for the 8 primitive types (e.g., Integer for int) An adapter class is used when the interface of an
FIU - CS - 3530
Packages Group of related classes. Specified by package statement. Fewer restrictions on access among each other; if class is called public, then it is visible to all classes if no visibility modifier is specified, it is equivalent to the frien
FIU - CS - 3530
Notes on access restrictions A source code file MyClass.java is a compilation unit and can contain at most one public class. Furthermore, if there is a public class in that file, it must be called MyClass. Upon compilation, a .class file is created
FIU - CS - 3530
Useful List Operations Return item from position j Search for item x Add (anywhere) Insert at position j; Insert at position 0 (or size-1) Add before (after) item x Remove any item Remove item in position j; Remove last (first) item Remove
FIU - CS - 3530
package weiss.util; / Fig 6.9-10, pg 192-4. public interface Collection extends java.io.Serializable { int size( ); boolean isEmpty( ); boolean contains( Object x ); boolean add( Object x ); boolean remove( Object x ); void clear( ); Iterator iterato
FIU - CS - 3530
How to insert into a linked listpublic class LinkedList extends AbstractCollection implements List {/ Insert newNode after q newNode.next = q.next; q.next = newNode; newNode.prev = q; newNode.next.prev = newNode; theSize+; public void add( int idx
FIU - CS - 3530
Stacks & Queues Implementationspublic class Stack implements Serializable { public Object push( Object x ) { items.add( x ); return x; } public Object pop( ) { if( isEmpty( ) ) throw new EmptyStackException( ); return items.remove( items.size( ) -
FIU - CS - 3530
Binary Treespublic class BinaryTree { static public void main( String [ ] args ) { BinaryTree t1 = new BinaryTree( "1" ); BinaryTree t3 = new BinaryTree( "3" ); BinaryTree t5 = new BinaryTree( "5" ); BinaryTree t7 = new BinaryTree( "7" ); BinaryTree
FIU - CS - 3530
Binary Treespublic void printPreOrder( ) { System.out.println( element ); / Node if( left != null ) left.printPreOrder( ); / Left if( right != null ) right.printPreOrder( ); / Right } public void printPostOrder( ) { if( left != null ) left.printPost
FIU - CS - 3530
Binary Search Trees/ BinarySearchTree class / / void insert( x ) -> Insert x / void remove( x ) -> Remove x / void removeMin( ) -> Remove minimum item / Comparable find( x ) -> Return item that matches x / Comparable findMin( ) -> Return smallest it
FIU - CS - 3530
Figure 8.3Basic action of insertion sort (the shaded part is sorted)Lecture 12Data Structures & Problem Solving using JAVA/2E Mark Allen Weiss1 2002 Addison WesleyFigure 8.4A closer look at the action of insertion sort (the dark shading ind
FIU - CS - 3530
package weiss.util; public class HashSet extends AbstractCollection implements Set { public HashSet( ); public HashSet( Collection other ); public int size( ); public Object getMatch( Object x ); public boolean contains( Object x ); private static bo
FIU - CS - 3530
import weiss.nonstandard.PriorityQueue; import weiss.nonstandard.PairingHeap; import weiss.nonstandard.BinaryHeap; class Edge { public Vertex dest; / Second vertex in Edge public double cost; / Edge cost public Edge( Vertex d, double c ) { dest = d;
FIU - CS - 3530
Permutations Permutations on 3 elements: abc acb bac bca cab cba N! different permutations on N elementsLecture 161PermutationsPublic static void perm(Object [] a, int k, int m) { / generate all permutations of list[k:m] int j; if (k = m) pr