# Questions tagged [algorithm-analysis]

Questions about the science and art of determining properties of algorithms, often including correctness, runtime and space usage. Use the [runtime-analysis] tag for questions about the runtime of algorithms.

1,582 questions
Filter by
Sorted by
Tagged with
50 views

### Comparing asymptotic running time of two algorithms $\sqrt n$ and $2^{\sqrt{\log _{2}n}}$

Given two algorithms with their time-complexity $t_a(n)=\sqrt{n}$ and $t_b(n) = 2^{\sqrt{\log _{2}n}}$ and i have to show $t_b(n) = O(t_a(n))$. I´ve made a program to check this statement and it ...
122 views

### Why is my algorithm version so slow with this input?

Here I'm trying to do a comparison of two simple as possible algorithms, solving the symmetric travelling salesman problem, finding the optimal solution without the support of heuristics. I'm showing (...
11 views

### Learning algorithm analysis

Im learning order of algorithm For x>=2, and rand(x) is function that return 1 value from 1 to x-1 which have uniform probability $\frac{1}{x-1 }$ And max(x,y) output bigger value and min(x,y) output ...
48 views

### Algorithm Analysis - Binary Search Algorithm

The problem is from Data Structures and Algorithm Analysis Edition 3.2 (Java Version) Book from Clifford A. Shaffer. It is from the third chapter exercises, problem number 3.13.20. Below is how it is ...
22 views

### Partitioning a set based on binary predicate

Given a collection of objects $X = (x_0,x_1,...,x_{N-1})$ and a binary predicate $F$ which takes as parameters elements of the collection, find a better than $\mathcal{O}(N^2)$ algorithm which ...
21 views

### Dijikstra's algorithm with “hull” value catch

Whilst preparing for the CCC(Canadian Computing Competition), I encountered CCC 2015 Seniors problem 4, linked here. Anyway, the problem describes a set of vertices(points) numbered from $1$ to $N$, ...
253 views

### Sorting a large list of test scores

You have a large list (say N > 10000) of test scores which you would like to sort. The test scores are between 1 and 100. What is quickest way to sort the list? First thought. We have a O(N log N) ...
175 views

### Prove that the 2-approximation of a modified local search algorithm for max-cut is tight

Consider the following local search approximation algorithm for the unweighted max cut problem: start with an arbitrary partition of the vertices of the given graph $G = (V,E)$, and as long as you ...
9 views

### learning the private key by reusing same random variable k in ELgamal

i wonder: if for some reason, someone, say alice, sends unencrypted messages to bob and signs it using elgamal signature, can oscar,the adversary, gain knowledge of the private key if alice reused the ...
19 views

8 views

### Study of cache behaviour of algorithms on Virtualbox

I want to study certain cache oblivious algorithms and cache behaviour of some other algorithms I wrote in general. I want to understand, is it advisable, if I do this study in an virtualized ...
33 views

### What is the time complexity in solving a polynomial equation of degree N in one variable?

How easy/difficult(in terms of big-O) is it to solve polynomial equations of high degrees of N? Do apps like Desmos actually solve equations to get roots or do they approximate roots by iterating ...
23 views

### Practice question on the applications of flows and cuts

This question is from Erickson's textbook on algorithms, p. 376, question 18. Faced with the threat of brutally severe budget cuts, Potemkin University has decided to hire actors to sit in ...
31 views

### Analysis of Pan-cake sorting

i was implementing pan-cake sorting. We can implement it by taking largest element to start and flipping it recursively (Like selection sort). However it is mentioned that the A[i] has to be a ...
34 views

### In Big-O notation, what does it mean for T(n) to be upper bounded by something

I do not have much experience in mathematics but I would really like to grasp Big-O notation on its mathematical level. I already read What does the "big O complexity" of a function mean? ...
11 views

### equivalent sub-keys in DES encryption

i am trying to understand the DES cryptosystem and was wondering: what would've happened if all of the sub-keys were equal? does it reduce the security? can we actually find the keys if we know all ...
59 views

### How to prove that an algorithm has no deadlock

I need to mathematically prove that this algorithm is deadlock-free: ...
26 views

### Would an optimization version of the 3-partition problem also be strongly np-complete / np-hard?

Anyone know if an optimization variant of the 3-partition problem (as explained there) would also be strongly np-complete? This would be where the goal is to group a multiset whose size is evenly ...
34 views

### Can algorithms of arbitrarily worse complexity be systematically created?

We’ve all seen this: Can we get worse? Part 1: Can mathematical operations of increasing orders of growth be generated, with or without Knuth’s up-arrow notation? Part 2: If they can, can ...
74 views

### How to prove NP-completeness of this variant of the set cover problem?

The problem exactly: Suppose you're helping to organize a summer sports camp, and the following problem comes up. For each of the n sports offered at this camp, the camp is supposed to have at least ...
141 views

### Time Complexity for Nearest Neighbor Searches in kd-trees

Nearest neighbor searches in kd-trees run in logarithmic time, as shown by Friedman et al. However, I have some difficulty to fully understand the proof. In order to calculate the average number of ...
21 views

### degree distribution

Does anyone know how to compute node degree distribution in a graph ? I am talking about a large graph for example California road network and imagine we have some data such as number of nodes and ...
23 views

### Intersection of 2 arrays

Here is a question i came across : Given two arrays, write a function to compute their intersection.Here we will allow the duplicates. Note: Each element in the result should appear as many ...