- 9.9.1: In the backtracking algorithm for SAT, suppose that we always choos...
- 9.9.2: Devise a backtracking algorithm for the RUDRATA PATH problem from a...
- 9.9.3: Devise a branch-and-bound algorithm for the SET COVER problem. This...
- 9.9.4: Given an undirected graph G = (V, E) in which each node has degree ...
- 9.9.5: Local search for minimum spanning trees. Consider the set of all sp...
- 9.9.6: In the MINIMUM STEINER TREE problem, the input consists of: a compl...
- 9.9.7: In the MULTIWAY CUT problem, the input is an undirected graph G = (...
- 9.9.8: In the MAX SAT problem, we are given a set of clauses, and we want ...
- 9.9.9: In the MAXIMUM CUT problem we are given an undirected graph G = (V,...
- 9.9.10: Let us call a local search algorithm exact when it always produces ...
Solutions for Chapter 9: Coping with NP-completeness
Full solutions for Algorithms | 1st Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
Another term for the conidence coeficient.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
The amount of variability exhibited by data
Error of estimation
The difference between an estimated value and the true value.
A subset of a sample space.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .