'Exponential time' diaporamas de présentation

NP-completeness

NP-completeness. Algorithms and Networks. Today. Complexity of computational problems Formal notion of computations NP-completeness Why is it relevant? What is it exactly? How is it proven? P vs. NP Some animals from the complexity zoo. 1. Introduction.

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Propositional Satisfiability and Constraint Programming: A Comparative Survey

Propositional Satisfiability and Constraint Programming: A Comparative Survey. Authors: Lucas Bordeaux, Youssef Hamadi & Lintao Zhang ACM Computing Surveys, Dec 2006 Speaker: Pingyu Zhang CSE990 Advanced Constraint Processing, Fall 2009. Outline.

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BIG-O --- Algorithms

BIG-O --- Algorithms. Purpose: Be able to evaluate the relative efficiency of various algorithms that are used to process data We need to be able to evaluate all of the major sort and search algorithms as well as the various implementations of the Abstract Data Types.

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1.2.1 Complexity 2 nd edition When size matters

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K NAPSACK

K NAPSACK. Given positive integers v i and w i for i = 1, 2, ..., n. and positive integers K and W. Does there exist a subset S of {1, 2, ..., n} such that:. and. A special case: S UBSET S UM. Given positive integers v i for i = 1, 2, ..., n. and an integer K.

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Time Complexity

Time Complexity. Consider a deterministic Turing Machine which decides a language. For any string the computation of terminates in a finite amount of transitions. Initial state. Accept or Reject. Decision Time = #transitions. Initial state. Accept or Reject.

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Time Complexity

Time Complexity. We use a multitape Turing machine We count the number of steps until a string is accepted We use the O(k) notation. Example:. Algorithm to accept a string :. Use a two-tape Turing machine Copy the on the second tape Compare the and. Time needed:.

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Logics for Data and Knowledge Representation

Logics for Data and Knowledge Representation. Propositional Logic: Reasoning. Originally by Alessandro Agostini and Fausto Giunchiglia Modified by Fausto Giunchiglia, Rui Zhang and Vincenzo Maltese. Outline. Review of PL: Syntax and semantics Reasoning in PL Typical tasks Calculus

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CSE 326: Data Structures Lecture #20 Really, Really Hard Problems

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Algorithm Strategies

Algorithm Strategies. Fawzi Emad Chau-Wen Tseng Department of Computer Science University of Maryland, College Park. General Concepts. Algorithm strategy Approach to solving a problem May combine several approaches Algorithm structure Iterative  execute action in loop

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CSE 326: Data Structures: Graphs

CSE 326: Data Structures: Graphs. Lecture 24: Friday, March 7 th , 2003. Today. Finish NP complete problems Course evaluation forms. NP-Complete Problems. Recall: A Hamiltonean path = a paths that goes through each node exactly once How to find one ? Try out all paths.

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Algorithm Strategies

Algorithm Strategies. Nelson Padua-Perez Chau-Wen Tseng Department of Computer Science University of Maryland, College Park. General Concepts. Algorithm strategy Approach to solving a problem May combine several approaches Algorithm structure Iterative ? execute action in loop

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Growth Rates of Functions

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LING/C SC/PSYC 438/538

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CSCI 2670 Introduction to Theory of Computing

CSCI 2670 Introduction to Theory of Computing. November 16, 2004. Agenda. Last week Test This week Section 7.1 and possibly part of 7.2 Remainder of semester Chapter 7. Announcement. Revised homework assignment for next Tuesday 7.1, 7.2, 7.6, 7.9, 7.12 Test will be returned tomorrow.

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Algorithm Complexity

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Lecture 3

Lecture 3. Analysis of Algorithms, Part II. Plan for today. Finish Big Oh , more motivation and examples, do some limit calculations. Little Oh, Theta notation Start Recurrences . Ex.1 ch.1 in textbook Tower of Hanoi. Binary search recurrence.

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NP-Complete Problems

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Limits to Computation

Limits to Computation. How do you analyze a new algorithm? Put it in the form of existing algorithms that you know the analysis. For example, given 2 arrays, pair the smallest in each array, the next smallest, etc. Can be done by sorting each array and pairing first, second, etc.

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How To Give a PowerPoint Talk

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