Questions tagged [amortized-analysis]

A method in analysis of algorithms that considers the overall cost of a sequence of operations.

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Choosing potential function in amortized analysis

How should I think to choose the potential function in the amortized analysis? More specifically are there techniques or tips for choosing optimal or good potential functions?
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Analysis of Weighted Quick Union with Path Compression

I have searched the internet for an analysis of why WQUPC is amortized $O( m \alpha (n) ) $ for m operations on n nodes ( $\alpha ( n) $ is the inverse Ackerman function). I understand why it is $O ( ...
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Formal justification of the accounting method and its meaning

I'm reading through CLRS again and I was wondering if there's a formal justification or construction of the accounting method, explaining why it works. For some reason it seems to me that CLRS ...
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Amortized time complexity of append on a dynamic array that resizes according to geometric base 1.25?

I'm trying to prove that the amortized time complexity of appending to a dynamic array that resizes in accordance with capacity = $N$ to $N+\lceil{\frac{N}{4}}\rceil$ is $O(1)$. I'm assuming that ...
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Array counter with mimimum find

I need to implement data strucure such as array, but with the following interface: GetMin() - Returns the minimum from the array IncRight(index) - Increases all values from specified index to the end ...
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How to compute amortized complexity of n runs of Dijkstra's algorithm?

I'm trying to figure out how to compute an amortized complexity/ or complexity of this algorithm. We have a Graph which is oriented. And we are going to run Dijkstra's algorithm for finding a shortest ...
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What is hiding behind amortized constant delay enumeration?

The following may contain errors. It is precisely because I am not sure I understand the topic that I am asking questions. I do not have books about it and could not find an adequate reference on the ...
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When was the dynamic array first introduced as an example for amortized analysis?

I'm writing a report on amortized analysis, and I'm using the example of a dynamic array to explain each method. I think it would be nice to add a reference to when this example was first used, as it ...
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124 views

Sequence of operations of Union-Find of length $m$ ($n$ being the number of Make-Set operations) with time complexity in $\Omega(m\log n)$

In Union-Find with link-by-rank but no path compression find a sequence of operations Make-Set, Find, Union of length $m$, containing $n$ Make-Set operations, and with time complexity in $\Omega(m\log ...
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325 views

Accounting method vs Potential method for analysing an augmented stack and differences with standard complexity analysis

With reference to chapter 17 of CLRS, (Amortized analysis). I'm trying to understand the differences between the accounting method and the potential method. Let's start with standard analysis of the ...
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amortized analysis

I am trying to find a general solution for the given A,B,C in dynamic arrays. Those veriables presents factors in the following operations : given : c_i the size of the array after operation O_i (...
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Why is maximum size of root is 2n + 1 in Splay trees?

In the amortized analysis of Splaying in Dynamic trees, let us consider a splay tree $T$ with $n$ keys and $v$ be a node of $T$. We define $size(v)$ as the number of nodes in the subtree rooted at $...
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Calculating the cost for each operation in amortized analysis

According to what I've read in the CLRS book , we calculate the amortized cost for a complete set , and not for a single operation.But in an exam question , it was asked about an operation amortized ...
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Is it true that the potential method is usually the inverse of the accounting method in the context of amortized analysis?

I remember reading this somewhere (will post the source as soon as I find it), but was wondering, if anyone knows why this is true or has maybe an example to portray why this is the case.
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Potential method analysis for Insert and Extract-max on a Max heap data structure

Suppose that you do some sequence of operations on a max heap, in this case only Insert and Extract-max. Whenever the heap ...
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Splay tree amortized cost analysis

I am looking into the amortized analysis of splay trees and seem to be missing something. Pretty much every resource uses the accounting method which I believe I grasp. What confuses me is the part ...
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if binary heap potential function is c*size(binary heap)) then insert will not take O(logn)and extract min will not take O(1) amortized time

So i want to prove that if i choose a potential function for binary heap as any constant*size of the binary heap (n is the number of nodes) then my insert will not have O(logn) amortized cost and ...
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Analysis of Union-Find(Disjoint Sets)

I have been trying to learn more about amortized analysis. Recently I came across the Disjoint Sets or Union-Find structures. I am using union by rank and path comparison. The potential of such data ...
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Amortized cost of decimal counter

Can somebody tell me what the lowest amortized cost for the increment operation of a decimal counter is? I can show the costs are O(1) and with max amortized costs of 2 (similar to a binary counter), ...
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Amortised complexity of dynamic array using potential function

I'm trying to find out how potential function works. I'm trying to compute an amortised complexity of $n$ operations on dynamic array. To make it simple, assume, that we can't delete items and we can ...
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342 views

What is the amortized time complexity of inserting an element to this heap?

Assume you implement a heap using an array and each time the array is full, you copy it to an array double its size. What is the amortized time complexity (for the worst case) of inserting elements ...
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277 views

Custom binary counter supports only increment in $2^i$ values amortized analysis

I'm a having trouble analyzing this algorithm. This is a binary counter that supports only increments in $2^i$ values it's implemented in this way: starting from the $i$-th location change all the ...