A NPC Problem in ink recognition
Strokes Segmentation
Problem
Shirley D. Marinkas
Yiyan Xiong
Introduction
Digital
ink A digital representation of a
users writing that they input using a pen or
stylus on a tablet or mobile device screen
Strokes the inpu
VC Hamiltonian Cycle
VC:
Instance: a graph G = (V, E) and an integer k.
Question: Does there exist S V such that (1) |S| k, and (2) every edge has at least
one endpoint in S?
Let G = (V, E) and k be an arbitrary instance of VC. We will now create a new gr
VC Hamiltonian Cycle
VC:
Instance: a graph G = (V, E) and an integer k.
Question: Does there exist S V such that (1) |S| k, and (2) every edge has at least
one endpoint in S?
Let G = (V, E) and k be an arbitrary instance of VC. We will now create a new gr
Some thoughts and comments on the VC to Hamiltonian Circuit (Cycle) transformation.
1) for each edge uv, there is a 12 vertex component created. One "side" consists of "u"
vertices, and the other "v" vertices. A cycle has been formed with all the "u" vert
Problem: Subset Sum
Given: A set S = cfw_s1, s2, , sn, for n 1, of positive integers, and an integer B.
Question: Does there exist a subset of S whose items sum to B?
Denote an instance of this problem by a Boolean variable SS(s1, s2, , sn, B) which is
tr
Multiple Sequence
Alignment
By Yuan Li
Multiple Sequence
Alignment
Lots of foundational problems in molecular biology
are NP-hard
Multiple Sequence Alignment
Phylogeny Construction
DNA sequencing (Shorest Common Superstring)
RNA Structure Crossing Alignme
Some thoughts and comments on the VC to Hamiltonian Circuit (Cycle) transformation.
1) for each edge uv, there is a 12 vertex component created. One "side" consists of "u"
vertices, and the other "v" vertices. A cycle has been formed with all the "u" vert
The Evolution of a Hard Graph Theory Problem Secure Sets
Ron Dutton
Computer Science
University of Central Florida
A Secure Set of a graph is a set S of vertices with the property that for
every subset X of S, N[X] S contains as many vertices as there are
Size n
Time
complexity
function
10
20
30
40
50
60
n
0.00001
second
0.00002
second
0.00003
second
0.00004
second
0.00005
second
0.00006
second
n2
0.0001
second
0.0004
second
0.0009
second
0.0016
second
0.0025
second
0.0036
second
n3
0.001
second
0.008
seco
Register Machines
Factor Replacement Systems
Chris Ellis
Bruce Meeks, Jr.
Register Machines
Natural numbers stored in finite set of
registers (result in nth register)
Finite length programs of instructions labeled
1 to m
Two types of instructions:
INCr [
Register Machines
Computer Science Department
University of Central Florida
COP 6410
Register Machine Concepts
A register machine consists of a finite length
program, each of whose instructions is chosen from a
small repertoire of simple commands.
The i
1. Consider the set of indices
DEFINED = cfw_ f | x f(x) .
Use Rices Theorem to show that DEFINED is not decidable.
Hint: There are two properties that must be demonstrated.
Defined is not trivial as the index of S(x) = x+1 is in, but (x) = y [ y = y+1] i
1. Consider the set of indices
DEFINED = cfw_ f | x f(x) .
Use Rices Theorem to show that DEFINED is not decidable.
Hint: There are two properties that must be demonstrated.
2. Let P = cfw_ f | x f(x) converges in at most x steps . Why
does Rices theorem
Primitive Recursive Turing
Machine
Every instance of Primitive Recursive can be replaced by an equivalent
instance of Turing Machine
Primitive Recursive
Base functions
Composition
Iteration
Bounded Minimization
Turing Computable
a Turing computation of so
Outline
Introduction
Primitive Recursive Models
Definition
Examples
Incomplete and Complete Models
Ackermanns Function
-Recursive Functions
Conclusion
Introduction
A recursive function is one that calls upon itself to
determine the solution
Fibonacci Numb
The Evolution of a Hard
Graph Theory Problem
Click to edit Master subtitle style
7/15/11
11
Many real world problems involve a
collection of entities (e.g.,
individuals, businesses, or countries)
that compete for each others
resources.
A group of these e
Complexity analysis of Evolution of Dual
Preference Orderings in Games of
International Conflict
Ramya Pradhan
April 15, 2010
Overview
Overview
Introduction
Motivation
Modeling
Complexity Analysis
Implication of Complexity Analysis
References
Introduction
Create a Formal Problem from a Real-world Problem
Investigate Complexity of Dened Problem
Redene the Problem
NP-Completeness for Revised Problem
References
COT 6410: Pipeline Scheduling
Michael Gabilondo
Michael Gabilondo
COT 6410: Pipeline Scheduling
Cre
Order Notation
Big "Oh"
Let f(n) and g(n) be two real valued functions over the integers n 1. (Sometimes, it
may be advantageous to allow n to be real. But, for our purposes, n usually will be the
"size" of a problem instance which is normally an integer.
Computability
The study of what can/cannot
be done via purely mechanical
means
History
The Quest for Mechanizing
Mathematics
Hilbert, Russell and Whitehead
Late 1800s to early 1900s
Axiomatic schemes
Axioms plus sound rules of inference
Much of focus
LOWER BOUND THEORY
Searching ordered lists with ComparisonBased Algorithms
Comparison-Based Algorithms: Information can be gained only by comparing keyto
element, or elementtoelement (in some problems).
Given: An integer n, a key, and an ordered list of n
Real World
NP-Complete Problems
Computer Science Department
University of Central Florida
COP 6410
Jonathan Cazalas & Tracy Bierman
Outline
Real World Problem
Explain problem
Optimization problem
Decision problem
Show Problem is NP-Complete
Is proble
Vertex Cover:
Data Structure:
n: number of vertices
m[1.n][1.n]: Adjacency matrix,
B: number giving target length of dominating set
Length
O(n^2) elements
We dont need the exact number. We just need a polynomially-related estimate.
Witness
w: Finite but u
HALTING PROBLEM given a syntactically correct program P and an input string of
characters X (X may or may not be a valid input for P it doesn't matter).
o Question does P halt when given X?
o P may loop forever or halt
So, is there an algorithm for the H
HALTING PROBLEM given a syntactically correct program P and an input string of
characters X. (X may or may not be a valid input for P it doesn't matter)
o Question does P halt when given X?
o P may loop forever or halt
So, is there an algorithm for the H