Applications of types of SATs Arash Ahadi 2013. What is SAT?

Slides:



Advertisements
Similar presentations
Lecture 24 MAS 714 Hartmut Klauck
Advertisements

Approximation Algorithms
Orthogonal Drawing Kees Visser. Overview  Introduction  Orthogonal representation  Flow network  Bend optimal drawing.
Graph Vertex Colorability & the Hardness Mengfei Cao COMP-150 Graph Theory Tufts University Dec. 15 th, Presentation for Final Project.
The Theory of NP-Completeness
Geometry Chapter Polygons. Convex Polygon – a polygon with a line containing a side with a point in the interior of the polygon.
CSC5160 Topics in Algorithms Tutorial 2 Introduction to NP-Complete Problems Feb Jerry Le
Introduction to Approximation Algorithms Lecture 12: Mar 1.
Computability and Complexity 15-1 Computability and Complexity Andrei Bulatov NP-Completeness.
What is the next line of the proof? a). Let G be a graph with k vertices. b). Assume the theorem holds for all graphs with k+1 vertices. c). Let G be a.
NP-Complete Problems Reading Material: Chapter 10 Sections 1, 2, 3, and 4 only.
NP-Complete Problems Problems in Computer Science are classified into
P versus NP and Cryptography Wabash College Mathematics and Computer Science Colloquium Nov 16, 2010 Jeff Kinne, Indiana State University (Theoretical)
1 CSE 417: Algorithms and Computational Complexity Winter 2001 Lecture 23 Instructor: Paul Beame.
Last class Decision/Optimization 3-SAT  Independent-Set Independent-Set  3-SAT P, NP Cook’s Theorem NP-hard, NP-complete 3-SAT  Clique, Subset-Sum,
1 CSE 417: Algorithms and Computational Complexity Winter 2001 Lecture 24 Instructor: Paul Beame.
Coloring Algorithms and Networks. Coloring2 Graph coloring Vertex coloring: –Function f: V  C, such that for all {v,w}  E: f(v)  f(w) Chromatic number.
Clique Cover Cook’s Theorem 3SAT and Independent Set
What is the next line of the proof? a). Assume the theorem holds for all graphs with k edges. b). Let G be a graph with k edges. c). Assume the theorem.
1 The Theory of NP-Completeness 2 NP P NPC NP: Non-deterministic Polynomial P: Polynomial NPC: Non-deterministic Polynomial Complete P=NP? X = P.
Chapter 15 Graph Theory © 2008 Pearson Addison-Wesley.
9.8 Graph Coloring. Coloring Goal: Pick as few colors as possible so that two adjacent regions never have the same color. See handout.
People Fractions. Problem 1 of 20 Answer 1 = 10 Problem 2 of 20 Answer 2 = 5.
Approximation Algorithms Department of Mathematics and Computer Science Drexel University.
1 The Theory of NP-Completeness 2012/11/6 P: the class of problems which can be solved by a deterministic polynomial algorithm. NP : the class of decision.
The minimum reload s-t path/trail/walk problems Current Trends in Theory and Practice of Comp. Science, SOFSEM09 L. Gourvès, A. Lyra, C. Martinhon, J.
The minimum reload s-t path/trail/walk problems Current Trends in Theory and Practice of Comp. Science, SOFSEM09 L. Gourvès, A. Lyra, C. Martinhon, J.
RESOURCES, TRADE-OFFS, AND LIMITATIONS Group 5 8/27/2014.
INHERENT LIMITATIONS OF COMPUTER PROGRAMS CSci 4011.
On s-t paths and trails in edge-colored graphs L. Gourvès, A. Lyra*, C. Martinhon, J. Monnot, F. Protti Lagos 2009 (RS, Brazil)
1 3-COLOURING: Input: Graph G Question: Does there exist a way to 3-colour the vertices of G so that adjacent vertices are different colours? 1.What could.
Instructor: Shengyu Zhang 1. Tractable While we have introduced many problems with polynomial-time algorithms… …not all problems enjoy fast computation.
Techniques for Proving NP-Completeness Show that a special case of the problem you are interested in is NP- complete. For example: The problem of finding.
1 Graph Coloring: An Overview Graph Coloring Basics Planar/4-color Graphs Applications New Register Allocation Technique.
1 The Theory of NP-Completeness 2 Cook ’ s Theorem (1971) Prof. Cook Toronto U. Receiving Turing Award (1982) Discussing difficult problems: worst case.
Paths and Trails in Edge Colored Graphs Latin-American on Theoretical Informatics Symposium LATIN 2008 Abouelaoualim, K. Das, L. Faria, Y. Manoussakis,
Problems on Paired Graphs Stephen Hedetniemi, Alice McRae, Dee Parks, Kelly Wise and come join in…
The Game of Cubic is NP-complete Erich Friedman Stetson University.
Graph.
CPS Computational problems, algorithms, runtime, hardness (a ridiculously brief introduction to theoretical computer science) Vincent Conitzer.
1 CPSC 320: Intermediate Algorithm Design and Analysis July 30, 2014.
NPC.
NP-Completeness Note. Some illustrations are taken from (KT) Kleinberg and Tardos. Algorithm Design (DPV)Dasgupta, Papadimitriou, and Vazirani. Algorithms.
Computational Complexity Shirley Moore CS4390/5390 Fall 2013 August 27, 2013.
1 CPSC 320: Intermediate Algorithm Design and Analysis July 30, 2014.
1 The Theory of NP-Completeness 2 Review: Finding lower bound by problem transformation Problem X reduces to problem Y (X  Y ) iff X can be solved by.
Computability Examples. Reducibility. NP completeness. Homework: Find other examples of NP complete problems.
Great Theoretical Ideas in Computer Science.
+ Angle Relationships in Triangles Geometry Farris 2015.
Hongyu Liang Institute for Theoretical Computer Science Tsinghua University, Beijing, China The Algorithmic Complexity.
34.NP Completeness. Computer Theory Lab. Chapter 34P.2.
Geometry 7-R Unit 7 Area Review Problems
A Graph Theoretic Approach to Cache-Conscious Placement of Data for Direct Mapped Caches Mirza Beg and Peter van Beek University of Waterloo June
Presented By Ravindra Babu, Pentyala.  Real World Problem  What is Coloring  Planar Graphs  Vertex Coloring  Edge Coloring  NP Hard Problem  Problem.
ICS 353: Design and Analysis of Algorithms NP-Complete Problems King Fahd University of Petroleum & Minerals Information & Computer Science Department.
Characteristics of Planar Graphs
COMPLEXITY THEORY IN PRACTICE
Hard Problems Introduction to NP
What is the next line of the proof?
Computability and Complexity
ICS 353: Design and Analysis of Algorithms
Subhash Khot Theory Group
Graph Theory Graph Colorings.
Richard Anderson Lecture 27 NP Completeness
Chapter 15 Graph Theory © 2008 Pearson Addison-Wesley.
Complexity Theory in Practice
Richard Anderson Lecture 25 NP Completeness
The Complexity of Approximation
Lecture 2-6 Complexity for Computing Influence Spread
Lecture 23 NP-Hard Problems
Presentation transcript:

Applications of types of SATs Arash Ahadi 2013

What is SAT?

What is SAT Problem?

SAT is NP-complete

Why 3-SAT is useful?

An example (in Computational Geometry)

An important open problem

Sketch of Proof

Types of SAT Why do we need another types of SATs?

Answer by several examples

Sketch of Proof

Planar 3-SAT

Other types and examples?!!

Labeling of Graphs: Lucky labeling

Existance

Hardness

Sketch of Proof

What about every k >1?

Main Reference

Another type Not All Equal SAT

Labeling of Graphs: Sigma labeling

The Relationship between Lucky & Sigma

They are very different

Relationship to Chromatic Number

Complexity for 3-regular graphs

Sketch of Proof

Complexity for every k

Minimizing the size of a Part

Conclusion

The Others

Proper Labeling Problems A.Ahadi and A. Dehghan, Journal of Theoretical Computer Science, in appears.

Edge Labeling by Sum

Proper Labeling Problems

Edge Labeling by Product

Vertex Labeling by Product

Edge Labeling by Gap

Vertex Labeling by Gap

Polynomial Algorithm

Fractional Coloring

The Results (in labelings)

There are several another theorems…

Thanks

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com Inc. All rights reserved.