# Questions tagged [analysis-of-algorithms]

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### What is the relevance of Real Analysis in TCS?

I'm a recent Math major who switched to a double major with Computer Science. I'm petitioning my CS Department Chair to allow me to take Real Analysis in place of Algorithms. I've already taken Data ...
• 369
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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 ...
• 111
1 vote
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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 ...
1 vote
106 views

### Which is the most efficient of the two following approximation algorithms?

Let $\mathfrak{B}$ be a set, which will be called the set of bins. Suppose we have five maps \begin{align*} \mathrm{Value} &: \mathfrak{B} \to \mathbb{R} \\ \mathrm{Upper} &: \mathfrak{B}...
• 111
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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 $S_i$ ...
• 21
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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 ...
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1 vote
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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 ...
• 225
542 views

### Most efficient inplace merge algorithms (stable and unstable)

I am currently researching the best algorithms available to achieve an inplace merge operation: consider two consecutive sorted arrays of size n and ...
• 307
3k views

### Random walk and mean hitting time in a simple undirected graph

Let $G=(V,E)$ be a simple undirected graph on $n$ vertices and $m$ edges. I'm trying to determine the expected running time of Wilson's algorithm for generating a random spanning tree of $G$. There, ...
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1 vote
312 views

### Complexity analysis on a parameterized recurrence relation

In order to analyse the complexity of our algorithm, we try to solve this recurrence: $T(n)=3T(n-1)-T(n-2)+T(n-k)+3^k$ ; in which $k$ is a parameter to be fixed. We know that this kind of ...
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344 views

### How to treat dynamic memory allocation in algorithm analysis?

I have an algorithm in which I want to dynamically allocate some memory. Let's say that I have N numbers and that I want to describe some binary relation over them. To do so I want to create a N*N ...
• 121
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### Travelling sales man with Quantum Computers [closed]

I know that it takes billions of years to solve the travelling sales man when n = 25 (Number of cities). I am wondering how fast can a quantum computer solve the travelling sales man problem (for ...
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### What is the state of the art research in analysing algorithms on GPU architectures?

I have found many papers on sequential algorithms that have been implemented and tested on GPU architectures. Each of these papers usually as a result contains the amount of speedup that was achieved ...
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1 vote