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Questions tagged [analysis-of-algorithms]

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Monotonic and bounded sequences throughout computer science

When I refer to the Monotone Convergence Theorem below, I refer to the very simple claim that if a non-decreasing sequence has an upper bound then it converges. I don't refer to the claim from Measure ...
wlad's user avatar
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2 votes
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Dynamic connectivity with known history, for maximal connected component span

Consider a graph in which edges are added and removed over time. Define the span of a connected component as the product of its number of vertices and the longest duration for which it remains a ...
Matthieu Latapy's user avatar
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Is there any research on the complexity of producing given a problem description?

It is straightforward enough to analyze the complexity of a particular algorithm as a function of input size or other variables in terms of runtime or space used or whatever else. I am wondering if ...
Joel Croteau's user avatar
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Tricky big-O calculation

I have a recursive algorithm in which the time for each step depends on the time for smaller steps. Essentially a structure is built at steps 1, 2, ..., n which must be searched at larger heights: $$ ...
Charles's user avatar
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Why does splitting $n$ bit integers into chunks of size $\log(n)$ specifically, help in multiplying them

In integer multiplication algorithms such as the Schonhage-Strassen algorithm (and the recently described Harvey and van der Hoeven algorithm), integers of size $n$ are reduced to polynomials with ...
Vighnesh Iyer's user avatar
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Computational complexity of polynomial interpolation with k non-zero terms

I am attempting to find a complexity for computing the order polynomial of partially ordered sets on a special family, and have come across the following problem. Assume we have the following values ...
Max Hopkins's user avatar
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Complexity of an algorithm involving permutations

I'm looking to figure out the computational complexity of an algorithm in an application I've written. The application computes the answer to a problem that is $\#P$-hard, and the algorithm I'm asking ...
Matt Samuel's user avatar
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Frogs Game Amortized Analysis

The game is defined by two integer parameters: n and k. We are given an array of n sets: $$S_1, S_2, ...., S_n$$ such that, each of them is a subset of $\{1, 2, ..., k\}$. Adversary picks a set $S_i$ ...
R.hatam's user avatar
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