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Topic: Asymptotic time complexity

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	Asymptotic analysis - Wikipedia, the free encyclopedia
		The asymptotic point of view is basic in computer science, where the question is typically how to describe the resource implication of scaling-up the size of a computational problem, beyond the 'toy' level.
		An asymptotic expansion of a function f(x) is in practice an expression of that function in terms of an infinite series, the partial sums of which do not (necessarily have to) converge; but such that taking any initial partial sum provides an asymptotic formula for f.
		Asymptotic expansions typically arise in the approximation of certain integrals (saddle-point method, method of steepest descent) or in the approximation of probability distributions (Edgeworth series).
	en.wikipedia.org /wiki/Asymptotic_behavior (359 words)

	AKS primality test - Wikipedia, the free encyclopedia
		As with any such algorithm, the paper concerned itself with establishing two facts: proving that the algorithm was correct, and establishing its asymptotic time complexity.
		This was achieved by proving two key facts, first by showing that an appropriate r can always be found and establishing an upper bound on its magnitude, and second by showing that the multiple equalities tested in the second part of the algorithm are sufficient to guarantee whether n is prime or composite.
		Since the running time of both parts of the algorithm is entirely dependent on the magnitude of r, proving an upper bound on r was sufficient to show that the asymptotic time complexity of the algorithm is O(log
	en.wikipedia.org /wiki/AKS_primality_test (876 words)

	Technical Report Abstracts
		The sequential algorithm known for this problem has time complexity O(mn) where m is the number of directed edges and n is the number of vertices in the given digraph.
		We then present a time sequential algorithm to solve the closed partition problem for a general planar digraph where n is the number of vertices in the given digraph.
		In this paper, we disprove the common assumption that the time for broadcasting in a mesh is at best proportional to the square root of the number of processors, at least in the presence of worm-hole routing.
	www.cs.utexas.edu /ftp/pub/techreports/INDEX/html/Abstracts.1991.html (6607 words)

	Fast Implementation Time Complexity Evaluation
		Section 3.1.1 depends on the time complexity of the priority queue operations.
		PQInsert(n) is the function describing the asymptotic time complexity of the insert an element operation of the priority queue.
		PQDelete(n) is the function describing the asymptotic time complexity of the delete an arbitrary element operation of a priority queue.
	www.cs.rit.edu /~std3246/thesis/node20.html (187 words)

	Asymptotic complexity - DmWiki
		For algorithms which take an input of varying size (for instance, algorithms that operate on a list of n elements), the algorithm's asymptotic complexity is a measure of how strongly or weakly the amount of time needed to finish the algorithm depends on the size n of the input.
		The notation used to describe asymptotic complexity is called "big-O notation".
		To be technical, to say that a function is O(f(n)) means that the time taken by the function is less than some constant times f(n).
	www.devmaster.net /wiki/Asymptotic_complexity (195 words)

	[No title]
		Then the time satisfies the recursion: $T(n)= a T(n/b) + f(n)$, where $f(n)$ is the total time in the non-recursive parts, the ``divide'' part and the ``conquer'' part.
		Thus, the total time is $T(n) \in O(f(n) \log n)$, since $b>1$ is a constant.
		The argument is simple algebra, and the same as the one that constants in front of the additive part don't affect the asymptotic time.
	www-cse.ucsd.edu /classes/sp04/cse202/dncsteps (1231 words)

	CS514 Lab 2
		You will analyze their time complexities and give a thorough justification in a lab report.
		Explain the shortcomings of asymptotic notation, especially regarding the hiding of constant factors, when two algorithms have the same asymptotic time complexities, using any relevant evidence from Part II to support your answer.
		Describe how this could affect the time complexity estimates you provided in Part I, and argue whether or not they had an effect on the time complexities based on your results from Part II.
	www.cs.wustl.edu /~raa4/CS514_FL00/labs/lab2 (1166 words)

	Asymptotic complexity
		The number of steps an algorithm requires to solve a specific problem is denoted as the running time of the algorithm.
		In general, the running time depends on the size of the problem and on the respective input.
		In general, just the order of the asymptotic complexity is of interest, i.e.
	www.iti.fh-flensburg.de /lang/algorithmen/asympen.htm (600 words)

	TED Notepad - An expanding Notepad replacement
		Yes, it costs little time and space to build those tables, but it is worth the result.
		This leads to a quadratic time complexity of strcmp, which makes this algorithm the worst algorithm for this case.
		A note to an epilogue: As I have said before, I have used qsort for sorting even in spite of its possibility to gain a quadratic time complexity, so I have used this way of unique even in spite of its possibility to gain the same bad results.
	jsimlo.sk /notepad/techs.php (2131 words)

	CS286 -- Lab 1: Searching
		Be able to apply asymptotic time complexity analysis to choose among competing algorithms.
		You should write a C++ program that will search through text files for a given sequence of words and display all of the line numbers (of the file) on which the sequence of words was found.
		For example, your algorithms should not take in a string representing the whole file (pass one line at a time instead).
	people.msoe.edu /~taylor/cs286/lab1.htm (728 words)

	[No title]
		Note that O(n2) worst-case time is an upper bound and we have not given a lower bound limit.
		The case in which v is not in the array is a worst-case input for binary search because in this case the loop is not exited early and lg(n) iterations are required.
		Answer: The upper bound worst-cast running time is O(n2) since each element of array is checked at most once by two for loops that each iterate a maximum of n times.
	www.cs.uml.edu /~kdaniels/courses/ALG_404_F05/Chapter3ProblemsSol.doc (431 words)

	Programming Assignment 1
		In this lab we will use the actual machine to validate our run-time complexity analysis and asymptotic run-time complexity analysis by comparing worst case, best case, and average case run times for Merge Sort and Insertion Sort.
		You should implement the algorithms within a sorting class and then plot their time behavior as a function of n and compare this with plots of the expected behavior.
		What inputs are required to generate “average” complexity.
	web.umr.edu /~ff/classes/253/proj1.html (234 words)

	A Linear Time Approximation Scheme for the Job Shop Scheduling Problem - Jansen, Solis-Oba, Sviridenko (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		Abstract: We study the preemptive and non-preemptive versions of the job shop scheduling problem when the number of machines and the number of operations per job are fixed.
		These algorithms are the best possible for such problems in two regards: they achieve the best possible performance ratio since both problems are known to be strongly NP-hard; and they have optimum asymptotic time complexity.
		of it have proved to be useful in designing polynomial time approximation schemes for other scheduling problems as well, see e.g.
	citeseer.ist.psu.edu /410129.html (600 words)

	CSC 282 Data Structures and Algorithms (3)
		To evaluate the merits of competing algorithms and competing data structures, based on asymptotic time complexity and time-space tradeoff.
		Asymptotic time complexity of a variety of algorithms.
		Linear and digraph data structures that use arrays and user-defined abstract data types.
	www.messiah.edu /departments/mathsci/courses/syllabi/CSC282.html (375 words)

	Cryptography - Asymptotic Complexity (Site not responding. Last check: 2007-11-01)
		is a deterministic polynomial time algorithm that evaluates
		is not an asymptotically one-way function, as it does not depend on security parameters.
		It is known that one-way functions are not sufficient for the following.
	rooster.stanford.edu /~ben/crypto/oneway.html (88 words)

	CS154, Assignment 8, Problem 1 Solution (Site not responding. Last check: 2007-11-01)
		This machine requires just n+1 steps to convert the input string, so the asymptotic time complexity is O(n), where n is the number of digits in the input string.
		By counting steps in the Turing machine above, we see that numbers that overflow take 4n+3 steps to convert, whereas numbers that do not overflow take just 2n+1 steps to convert.
		In both cases, then, the asymptotic time compexity is O(n), where n is the number of digits in the input string.
	graphics.stanford.edu /~dk/cs154.html (282 words)

	[No title]
		I did not understand why the author says utilisation of agent(u)= payment + valuation isnt it payment - valuation (the utility for an agent) summary: the authors try to use VCG mehcanism in order to fast compute the payment for the agents in the network.
		The aim of the agents is to maximize their utility function.
		The authors give an algorithm that improves upon a previous complexity algorithm.
	www.cs.pitt.edu /~utp/cs3150/lecture/questions4post.doc (817 words)

	[No title]
		Our two-layer channel router is designed to find solutions which minimize both wiring area and number of vias simultaneously.
		We also derive a bound for its access delay.
		Most methods simplify the problem by approximating the area source with a collection of point sources.
	www.cs.utexas.edu /ftp/pub/techreports/INDEX/OLD.INDEXES/index-1991 (4908 words)

	asymptotic time complexity (Site not responding. Last check: 2007-11-01)
		Definition: The limiting behavior of the execution time of an algorithm when the size of the problem goes to infinity.
		Note: From Algorithms and Theory of Computation Handbook, page 19-26, Copyright © 1999 by CRC Press LLC.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "asymptotic time complexity", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/asymptoticTimeComplexity.html (119 words)

	Linear-Time Rule Induction - Domingos (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		These are able to efficiently process large numbers of examples, under the constraint of still achieving good accuracy.
		If e is the number of examples, many rule learners have O(e 4) asymptotic time complexity in noisy domains, and C4.5RULES has been empirically observed to sometimes require O(e 3).
		Recent advances have brought this bound down to...
	citeseer.ist.psu.edu /15238.html (518 words)

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