having learned some about algorithm analysis in my discrete structres class..Ive been wondering how other functions are affected by big O...could you have a O (1/x^2) ?....or even better... O(1/n!)...the once infamous runtime that everyone avoided would soon become the one everyone sought to acheive (as if O(1) could get any better)
It caught my attention and I thought it deserved a post on this website..so my questions are:
Can you have O(1/ some complexity ex..n^2 b^n n^b etc...)
and if so, what kind of loop would this be, i know that doubling or halving would result in log n or n log n time but not sure about 1/ anything
2 Replies  1513 Views  Last Post: 25 February 2007  06:00 AM
Replies To: analysis of algorithms
#2
Re: analysis of algorithms
Posted 20 February 2007  01:26 AM
mattman059, on 19 Feb, 2007  09:53 PM, said:
having learned some about algorithm analysis in my discrete structres class..Ive been wondering how other functions are affected by big O...could you have a O (1/x^2) ?....or even better... O(1/n!)...the once infamous runtime that everyone avoided would soon become the one everyone sought to acheive (as if O(1) could get any better)
It caught my attention and I thought it deserved a post on this website..so my questions are:
Can you have O(1/ some complexity ex..n^2 b^n n^b etc...)
and if so, what kind of loop would this be, i know that doubling or halving would result in log n or n log n time but not sure about 1/ anything
It caught my attention and I thought it deserved a post on this website..so my questions are:
Can you have O(1/ some complexity ex..n^2 b^n n^b etc...)
and if so, what kind of loop would this be, i know that doubling or halving would result in log n or n log n time but not sure about 1/ anything
Hi
If you have a think about linear programming, any processing with an algorithm will never meet the criteria to meet 1/n or smaller Big O timings. The program must have an increasing function against time purely because of n and the iterations.
If you used a threaded solution, however, the potential for 1/2, 1/3 1/4(n) is there, related to the total processing power and how well the parallelism operates. Some older CPU (and OS's) may not be capable of delivering true multithreaded capability.
You should also consider the effect of increasing the loading (n) in multithreaded programs. There is a point at which the machine will be running to many processes and simply bog down with context switching and memory swapping. Taking you from say O(1/4n) to O(n^2) very quickly (based on time to complete the processing).
Finally, there is a recommended limit of 16 independent threads in your process. While I have run 101 threads attached to a process, there was a clear level of latency (like 4 seconds) that was clearly visible in the logs after running. Also, my threads required a level of synchronisation because access to the logs was restricted to one thread at a time.
hope this helps.
#3
Re: analysis of algorithms
Posted 25 February 2007  06:00 AM
Althogh my backgound is in mathematics and I should LOVE BIGO I really don't. I think that is because the engineers love math where you can throw out unimportant numbers and I hate to throw out numbers. I don't know, it is a personal prejudice that I should really get over.
Anyway the concept of a O(1/n) essentialy means that the process gets FASTER the longer the input is. There are some algorithms that "seem" to offer such a feat, such as searching though a text document of size M. THe longer our seach string (length N) the faster a Boyer–Moore search will go. When this is brought up for the first time there is always at least one student who thinks that this will have a complexity like O(1/N). I was one of these lucky dunces.
I know that this is an O(n) algorithm, but I can't explain exactly why.
This is why I hate BigO (though I did ace all of my tests on it in school, then promptly forgot all I knew about using recurrence relations to calculate BigO)
Anyway the concept of a O(1/n) essentialy means that the process gets FASTER the longer the input is. There are some algorithms that "seem" to offer such a feat, such as searching though a text document of size M. THe longer our seach string (length N) the faster a Boyer–Moore search will go. When this is brought up for the first time there is always at least one student who thinks that this will have a complexity like O(1/N). I was one of these lucky dunces.
I know that this is an O(n) algorithm, but I can't explain exactly why.
This is why I hate BigO (though I did ace all of my tests on it in school, then promptly forgot all I knew about using recurrence relations to calculate BigO)
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