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	Amortized analysis (Site not responding. Last check: 2007-10-21)
		There are several techniques used in Amortized analysis: # Aggregate analysis - determines upper bound T(n) on total cost of sequence of ''n operations, then calculates average cost to be T(n)/n'' # Accounting method - determines the individual cost of each operation.
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		Stock Technical Analysis Technical analysis techniques such as candlestick charting, fibonacci numbers, volume analysis and market indicators explained and exploited.
	www.serebella.com /encyclopedia/article-Amortized_analysis.html (481 words)

	[No title]
		Amortized analysis is a way of proving that even if an operation is occasionally expensive, its cost is made up for by other, cheaper occurrences of the same operation.
		Amortized Analysis of Hash Tables --------------------------------- Suppose that every operation (insert, find, remove) takes one dollar of actual running time unless the hash table is resized.
		Amortized analysis (as presented here) only tells us an upper bound (big-Oh) on the actual running time, and not a lower bound (big-Omega).
	www.cs.berkeley.edu /~jrs/61bs04/lec/38 (1246 words)

	amortized analysis (Site not responding. Last check: 2007-10-21)
		Amortized analysis: no involvement of probability performance on a sequence of even some operation was expensive.
		Three Methods of analyss Aggregate analysis: Total cost n operations/n, Accounting method: Assign type of operation an (different) amortized overcarge some operations, store the overcarge as credit on specific then use the credit for for some later operations.
		Amortized cost in aggregate is defined to be average Another example: increasing a counte Binary counter of length k, a0..k-] of bit array.
	www.onhomeloans.net /amortizedanalysis.htm (349 words)

	Amortized analysis - Wikipedia, the free encyclopedia
		For other uses of the term Amortization, see the Amortization disambiguation page.
		In analysis of algorithms, amortized analysis refers to finding the average running time per operation over a worst-case sequence of operations.
		Aggregate analysis determines the upper bound T(n) on the total cost of a sequence of n operations, then calculates the average cost to be T(n)/n.
	en.wikipedia.org /wiki/amortized_analysis (139 words)

	Greedy Algorithms (Site not responding. Last check: 2007-10-21)
		n an amortized analysis, the time required to perform a sequence of data structure operations is average over all operation performed.
		Amortized analysis can be used to show that average cost of an operation is small, if one average over a sequence of operations, even though a single operation might be expensive.
		Unlike the average probability distribution function, the amortized analysis guarantees the 'average' performance of each operation in the worst case.
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/Amortized/amortizeIntro.htm (138 words)

	CMSC 335 Advanced Data Structures
		Associating a potential function with the data structure and evaluating the amortized cost of each operation as the cost of the operation plus the change in potential caused by the operation.
		The first method of analysis is to simply add up the cost of n successive operations, divide by the number of operations, n, and obtain the average or amortized cost per operation.
		The most difficult aspect of using amortized analysis to study the realistic costs involved in a sequence of operations on a data structure is to find an appropriate potential function.
	www.academic.marist.edu /jte/ads/AmortizedAnalysis.htm (1245 words)

	Intro to Algorithms: CHAPTER 18: AMORTIZED ANALYSIS (Site not responding. Last check: 2007-10-21)
		In an amortized analysis, the time required to perform a sequence of data-structure operations is averaged over all the operations performed.
		If we want analysis with amortized costs to show that in the worst case the average cost per operation is small, the total amortized cost of a sequence of operations must be an upper bound on the total actual cost of the sequence.
		Using amortized analysis, we shall show that the amortized cost of insertion and deletion is only O(1), even though the actual cost of an operation is large when it triggers an expansion or a contraction.
	www.serghei.net /docs/programming/Cormen/chap18.htm (6536 words)

	Amortized Analysis (Site not responding. Last check: 2007-10-21)
		Amortized Cost: If the time complexity to perform n operations is T(n) in the worst case, then the amortized cost per operation is T(n)/n.
		Then, the amortized cost for a PUSH is 2,since the real cost is 1, and the amortized cost for a POP is 0, since for the POP operation, the real cost is 1 and the change in potential is -1 since the number of items decreases.
		Amortized analysis has thus shown that the cost of n operations for each of the 2 problems considered above is only O(n), which is way better than the naïve analysis performed initially.
	www.msci.memphis.edu /~giri/7713/f98/shanti.html (596 words)

	Introduction to Algorithms \| Chapter Overview - Chapter 17
		Amortized analysis can be used to show that the average cost of an operation is small, if one averages over a sequence of operations, even though a single operation within the sequence might be expensive.
		Amortized analysis differs from average-case analysis in that probability is not involved; an amortized analysis guarantees the average performance of each operation in the worst case.
		Section 17.3 discusses the potential method, which is like the accounting method in that we determine the amortized cost of each operation and may overcharge operations early on to compensate for undercharges later.
	highered.mcgraw-hill.com /sites/0070131511/student_view0/chapter17/chapter_overview.html (454 words)

	Amortized analysis (Site not responding. Last check: 2007-10-21)
		In computational complexity theory, Amortized analysis is the time per operation averaged over a worst-case sequence of operations.
		Amortized analysis differs from average-case performance in that probability is not involved; amortized analysis guarantees the time per operation over worst-case performance.
		There are several techniques used in Amortized analysis:
	www.webstercc.com /encyclopedia/en/wikipedia/a/am/amortized_analysis.html (110 words)

	Citations: Amortized computational complexity - Tarjan (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		for examples of amortized analysis) The space requirements are favourable: the algorithm uses O(n m) space for the representation of the graph and O(n) space to store the topological order; O(n) additional space is required during the execution of the update operation.
		A Systematic Analysis of Splaying - Schoenmakers (1993)
		For our amortized analysis, let us denote by q i the number of pairs inserted in Q during the i th execution of IPC and by q i = P i j=1 q i the total number of pairs inserted in Q during the first i executions of IPC.
	citeseer.ist.psu.edu /context/7162/0 (2832 words)

	Amortized Analysis History - Amortized Analysis Information
		Amortized analysis is an analysis technique that provides tight bounds on the worst-case running time of an algorithm that involves a sequence of possibly different operations.
		A naive analysis of the running time of this algorithm would have to conclude that the running time is O(k*n) since in the worst possible scenario the algorithm would apply a O(k) operation n separate times.
		The point of using all this amortized cost is that the total actual cost incurred by all the operations in sequence is actually equal to or less than the amortized cost incurred by all the operations.
	www.bookrags.com /sciences/computerscience/amortized-analysis-wcs.html (838 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Algorithm Analysis The key here is to attempt to count how many simple statements in an algorithm are executed for any input of a particular size, in terms of this input size.
		Amortized Analysis The key here is to not focus on the worst case performance of a single operation, but to look at the worst case performance of a string of several operations in a row.
		The two main examples we used amortized analysis for are the extendable table/array and the splay tree.
	longwood.cs.ucf.edu /courses/cop3530/spr2003/lectures/COP3530Exam1Review.doc (1767 words)

	Amortized analysis -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		In (Click link for more info and facts about computational complexity theory) computational complexity theory, amortized analysis is the time per operation averaged over a (Click link for more info and facts about worst-case) worst-case sequence of operations.
		Amortized analysis differs from (Click link for more info and facts about average-case performance) average-case performance in that (A measure of how likely it is that some event will occur) probability is not involved; amortized analysis guarantees the time per operation over worst-case performance.
		Potential method is like the accounting method, but overcharges operations early to compensate for undercharges later.
	www.absoluteastronomy.com /encyclopedia/A/Am/Amortized_analysis.htm (158 words)

	Chapter 4
		The lemma implies, that the given definition of amortized time is closely related to the intuitive definition of amortized time as being the average time per operation over a sufficiently long sequence of operations.
		The amortized cost of any of these operations, is equal to this cost plus the sum of the new potentials of all involved nodes minus the sum of their old potentials.
		The analysis of the memory usage is simple: the expected number of level j nodes is the same as before.
	www.cs.umu.se /~jopsi/dinf504/chap4.shtml (8427 words)

	SW5 Advanced Algorithm Design and Analysis (Site not responding. Last check: 2007-10-21)
		Thus, although the worst-case running time of a single operation may be high, the average cost of an operation in a sequence of operations may be much lower.
		Amortized analysis is used to find the average cost of an operation in a sequence of operations, but it differs from the average-case analysis in that probability is not involved.
		An amortized analysis guarantees the average performance of each operation looking at the worst-case running time of a sequence of n operations.
	www.cs.auc.dk /~simas/aalg04/lecture12.html (253 words)

	[No title]
		When we do asymptotic analysis, we often come up with an upper bound that is not tight and is not really fairly indicative of expected performance.
		Amortized analysis does not apply to all algorithms, only do those with a data structure that causes the algorithm to exhibit the characteristic that if it is invoked multiple times in a sequence, its performance will vary depending upon what step in the sequence is being executed.
		This differs from and is NOT an average case analysis because of the fixed predictable sequence of conditions; an average case analysis would be the presentation of random condition sets at each of n calls, i.e.
	ranger.uta.edu /~cook/aa/transcript/ln10f (1534 words)

	SI433 Class 21
		In class last time, we informally used what is called the "accounting method" of amortized analysis (Section 18.2 of your textbook).
		The trick with the accounting method is to fix an amortized cost for each operation, and show that the actual cost of a sequence of M operations does not exceed M times the amortized cost.
		Since the work of increment is essentially one plus the number of times you go through the loop, and since this is exactly the number of bits that get flipped by increment, the actual cost will be equal to the number of bits flipped.
	www.cs.usna.edu /~wcbrown/courses/S01SI433/classes/C21/Class.html (1144 words)

	Class Notes (Site not responding. Last check: 2007-10-21)
		In an amortized analysis, we are looking for the time bound for a sequence of operations, instead of the cost of a single operation.
		Amortized cost is the worst-case cost for a sequence of operations.
		We have an amortized cost for a single operation to be bounded by 3N/N=3.
	www.msci.memphis.edu /~giri/7713/f00/BoGuan/BoGuan.htm (1211 words)

	[No title]
		Motivation is that traditional worst-case-per-operation analysis can give overly pessimistic bound if the only way of having an expensive operation is to have a lot of cheap ones before it.
		E.g., we saw this with B-trees: when analyzing the cost to perform node-splits in an insert, we saw it could be up to O(depth*t) if we split at each level, but in sequence of n inserts, total cost spent on splitting nodes was just O(n), meaning constant time per insert on average for splitting.
		Neat amortized dictionary data structure: In last couple classes, looked at ways of storing information with O(log n)-cost search and inserts.
	www.cs.cmu.edu /afs/cs.cmu.edu/academic/class/15451-f99/www/lectures/lect0923 (646 words)

	Amortized (Site not responding. Last check: 2007-10-21)
		Amortized analysis can be used to show that the...
		Note: The term "amortized worst case" is sometimes used to emphasize that the worst case...
		Amortized Communication Complexity In this work we study the direct-sum problem with respect to communication complexity: Consider a relation f defined over f0; 1g n Theta f0; 1g n.
	www.yourdreammortgage.com /1/amortized-.htm (578 words)

	420 Review 1 (Site not responding. Last check: 2007-10-21)
		Amortized Analysis: the time per operation averaged over the worst-case sequence of operations.
		Aggregates Analysis: determines upper bound T(n) on the total cost of n operation, then calculates the average cost as T(n)/n (where T(n) = all work done in worst case sequence of n operations).
		B Tree: of order m is an m-way search tree/ m-ary balanced tree in which the root is either a leaf or has at least 2 non-empty children AND every internal node has between ceil(m/2) and m children (so m/2 to m-1 records) AND all leaves are at the same level.
	www.wam.umd.edu /~jtyler/420finalreview.html (2718 words)

	Computer Science - CS 410 Top: Algorithm Design & Analysis (4 credits) (Site not responding. Last check: 2007-10-21)
		Apply the concept of amortized analysis in straight forward cases.
		Analysis of algorithms, algorithm selection, associated mathematical techniques, concept of NP-completeness, techniques for proving algorithms are correct.
		A major goal of the course is to teach students to choose an appropriate algorithm to solve a problem.
	www.cs.pdx.edu /course.php?cid=273 (395 words)

	Amortized Analysis (Site not responding. Last check: 2007-10-21)
		Though the worst case performance of an algorithm may be f(n), the average worst case over n runs may be asymptotically less than n*f(n).
		We will study three methods for average worst case analysis:
		Show all n runs take a total worst case time T, thus the average worst case is T/n.
	ranger.uta.edu /~cook/aa/lectures/l10/node1.html (83 words)

	Amortized analysis
		Aggregate analysis[?] - determines upper bound T(n) on total cost of sequence of n operations, then calculates average cost to be T(n)/n
		Accounting method[?] - determines the individual cost of each operation.
		The text of this article is licensed under the GFDL.
	www.ebroadcast.com.au /lookup/encyclopedia/am/Amortized_time.html (117 words)

	No Title (Site not responding. Last check: 2007-10-21)
		Amortized analysis is a type of worst-case analysis.
		Amortized analysis is a type of average-case analysis.
		Amortized analysis is only applicable to lazy data structures (i.e., data structures in which some operations are delayed and carried out at lower cost as part of some other operations).
	www.cs.unm.edu /~crowley/phdExams/1991spring/th/th.html (1886 words)

	Hash table - Wikipedia, the free encyclopedia
		Enlarging the table means that effectively all the records in the hash table have to be added all over again.
		This is typically an expensive, albeit infrequent, operation; so the amortized time for each operation remains low.
		Some hash table implementations, notably in real-time systems, cannot pay the price of enlarging the table and must be initially allocated with enough space.
	en.wikipedia.org /wiki/Hashtable (2857 words)

	CPSC 517 - Topics (Site not responding. Last check: 2007-10-21)
		A worst case analysis of an algorithm is sometime more pessimistic than necessary: Inputs that cause an algorithm to use the time or space suggested by this kind of analysis might be infrequent, and one might be more interested in the way the algorithm works ``most of the time.''
		``Amortized analysis'' provides more meaningful information about the behaviour of certain data structures, when these are accessed or changed by a long sequence of operations.
		However there is, evidently, interesting material concerning the analysis of heuristics - including branch and bound algorithms, as well as more recent approaches such as genetic algorithms, that would be appropriate for inclusion in CPSC 517.
	pages.cpsc.ucalgary.ca /~eberly/Courses/CPSC517/topics.html (761 words)

	Machine Learning List: Vol. 7, No. 7 (Site not responding. Last check: 2007-10-21)
		This framework uses the methodology of amortized analysis to simultaneously derive an algorithm and obtain worst-case bounds on the algorithms predictive performance.
		With the tutorial we hope to reach experimentalist and teach them how to apply the new family to their problems and teach theoretically oriented researchers how amortized analysis can be used to analyze simple learning algorithms.
		Her research interests are in the use of local energy and phase congruency models for the detection and synthesis of image attributes, and in the use of vision for the measurement of biological shape and form.
	www.ics.uci.edu /~mlearn/MLlist/v7/7.html (9677 words)

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