'Hamiltonian cycle' presentation slideshows

Algorithm Design and Analysis (ADA)

Algorithm Design and Analysis (ADA). 242-535 , Semester 1 2013-2014. Objective look at the complexity classes P, NP, NP-Complete, NP-Hard, and Undecidable problems. 17. P and NP, and Beyond. Overview. A Decision Problem Polynomial Time Solvable (P ) Nondeterministic Polynomial (NP )

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Algorithms

Algorithms. NP-Complete Problems. Polynomial time algorithms. Most algorithms we have studied so far are polynomial time in the size of their inputs n. Worst case running time is O(n k ) for some constant k. Problems that are solvable by polynomial time algorithms are said to be tractable.

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Design and Analysis of Computer Algorithm Lecture 10

Design and Analysis of Computer Algorithm Lecture 10. Pradondet Nilagupta Department of Computer Engineering. Acknowledgement.

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The Theory of NP-Completeness

The Theory of NP-Completeness. Tractable and intractable problems NP-complete problems. The theory of NP-completeness. Tractable and intractable problems NP-complete problems. Classifying problems. Classify problems as tractable or intractable.

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CS 332: Algorithms

CS 332: Algorithms. NP Complete: The Exciting Conclusion Review For Final. Administrivia. Homework 5 due now All previous homeworks available after class Undergrad TAs still needed (before finals) Final exam Wednesday, December 13 9 AM - noon

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Analysis & Design of Algorithms (CSCE 321)

Analysis & Design of Algorithms (CSCE 321). Prof. Amr Goneid Department of Computer Science, AUC Part R5. Graphs. Graphs. Graphs. Basic Definitions Paths and Cycles Connectivity Other Properties Representation Spanning Trees. A. F. B. G. E. C. D. 1. Basic Definitions.

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Fault-tolerant cycle-embedding of crossed cubes

Fault-tolerant cycle-embedding of crossed cubes. Ming-Chien Yang a, Tseng-Kuei Li b , ?, Jimmy J.M. Tan a, Lih-Hsing Hsu a ?????? ???????? ??. Outline. Introduction Definitions and notation Main result Appendix A. Introduction.

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Lecture 21 Approximation Algorithms

Lecture 21 Approximation Algorithms. Introduction. Earlier Results on Approximations. Vertex-Cover Traveling Salesman Problem Knapsack Problem. Performance Ratio. Constant-Approximation. c-approximation is a polynomial-time approximation satisfying :

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CSC 413/513: Intro to Algorithms

CSC 413/513: Intro to Algorithms. NP Completeness Continued: Reductions. Review: P and NP. What do we mean when we say a problem is in P ? What do we mean when we say a problem is in NP ? What is the relation between P and NP ?. Review: P and NP.

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Lecture 24 NP-Complete Problems

Lecture 24 NP-Complete Problems. (1) Polynomial-time many-one reduction. A < m B. p. A set A in ? * is said to be polynomial-time many-one reducible to B in ? * if there exists a polynomial-time computable function f: ? * ? ? * such that

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Chapter 6. Relaxation

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Part V Theory of Approximate Computation

Part V Theory of Approximate Computation. Lecture 25 Approximation for NP-hard Problems. Earlier Results on Approximations. Vertex-Cover Traveling Salesman Problem Knapsack Problem. Performance Ratio. Constant-Approximation. c-approximation is a polynomial-time approximation satisfying :

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Sorting an Intransitive Total Ordered Set

Sorting an Intransitive Total Ordered Set. Sequential and Parallel Implementation for COMP 5704 Parallel Algorithms by Johannes Singler, Carleton University. Presentation Outline. Introduction to the Problem Prerequisites Sequential Algorithm Parallelizing for a PRAM Questions?!.

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The n-Queens Problem

The n-Queens Problem. The problem is to place n queens (chess pieces) on an n by n board so that no two queens are in the same row, column or diagonal The 4 by 4 board above shows a solution for n = 4 The text gives an explicit construction for a solution for each n ? 4 (page 202)

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Weighted Matching-Algorithms, Hamiltonian Cycles and TSP

Weighted Matching-Algorithms, Hamiltonian Cycles and TSP. Graphs & Algorithms Lecture 6. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A. Weighted bipartite matching. Given: K n , n (complete bipartite graph on 2n vertices)

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Proof of Euler's theorem Part 2 :

An Euler Circuit is a cycle of an undirected graph, that traverses every edge of the graph exactly once, and ends at the same node from which it began. Euler's Theorem : A connected graph G possesses an Euler circuit if and only if G does not contain any nodes of odd degree.

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Example: HP ? p HC

Example: HP ? p HC. Hamiltonian Path Input: Undirected Graph G = (V,E) Y/N Question: Does G contain a Hamiltonian Path? Hamiltonian Cycle Input: Undirected Graph G = (V,E) Y/N Question: Does G contain a Hamiltonian Cycle?. Specification of R(x).

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Theorem 6.4 1/4

Theorem 6.4 1/4. The Petersen graph is non-Hamiltonian. Proof ? [proof by contradiction]

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