Principles of Algorithm
Analysis
Biostatistics 615
Lecture 3
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Principles of Algorithm Analysis, Slides of Algorithms and Programming
Shun faster algorithms to avoid complexity in program. • Instead, wait for simple N2 algorithms, when N log N alternatives exist of modest complexity ...
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Principles of Algorithm
Analysis
Biostatistics 615
Lecture 3
Problem Set… z
Questions?
z
FAQ:
How to compile C code?
10 minute introduction for the adventurous…
GCC z
GNU C Compiler
Available on most UNIX systems
Also on newer Macintosh computers
z
For Windows, download from
www.mingw.org
www.cygwin.com
Running GCC z
Command line application z Basic usage is: gcc –o program_name source.c
Use extension “.c” or “.cpp” for source code z Reads in source(s), creates executableprogram
Good editors for C programs… z
Commercial compilers provide veryfancy editors
z
A good free alternative is
nedit
On Windows, available when you installcygwin.
Today z
Strategies for comparing algorithms
z
Common relationships betweenalgorithm complexity and input data
z
Compare two simple search algorithms
Specific Questions z
Compare two algorithms for one task z Predict performance in a new environment
If we had a computer that was 10x faster and couldhandle 10x more data, how would approach perform? z Set values of algorithm parameters
Two Common Mistakes z
Ignore performance of algorithm
Shun faster algorithms to avoid complexity in program
Instead, wait for simple
N
2 algorithms, when N log N alternatives exist of modest complexity available z Too much weight on performance of algorithm
Improving a very fast program is not worth it
Spending too much time tinkering with code is rarelygood use of time
Choices of Input Data z
Actual data
Measures performance in use
z
Random data
Generic approach, may not be representative
z
Perverse data
Attempt worst case analysis
Limitations of EmpiricalAnalysis z
Quality of implementation
Is our favored implementation coded morecarefully than another?
z
Extraneous factors
Compiler
Machine
Computer system
Theoretical Analysis z
Predict performance of algorithm basedon theoretical properties
z
“Independent” of actual implementation
z
Several constructs occur frequently inalgorithm analysis
Limitations of TheoreticalAnalysis z
Efficiency can depend on compiler
z
Efficiency may fluctuate with input data
z
Some algorithms are not well understood
Two typical analyses z
Average-case for random input
z
Worst-case
z
Are these representative of real worldproblems?
Check with empirical predictions…
The Primary Parameter
N
z Examples
Degree of polynomial
Number of characters in a string
Size of file to be sorted
Number of input data items
Some other abstract measure of problem size z With multiple parameters, we can often holdone of them constant