# Questions tagged [sorting]

Given a sequence of elements, find a permutation such that the elements are in a certain order.

109 questions
Filter by
Sorted by
Tagged with
890 views

### Enumerating topological sorts of a vertex-labeled DAG

Let $G = (V, E)$ be a directed acyclic graph, and let $\lambda$ be a labeling function mapping each vertex $v \in V$ to a label $\lambda(v)$ in some finite alphabet $L$. Writing $n := |V|$, a ...
74 views

### What would be the performance properties of a comb or shell sort where the gap sequence is the prime numbers?

In particular, the genesis of this idea was the notion that you could minimize the number of passes through the list in a comb sort by using the primes as a way to guarantee that every element gets ...
100 views

### A sorting algorithm that uses the minimum comparasions possible

I'm looking for a sorting algorithm that minimizes comparisons instead of time complexity. The algorithm shouldn't compare any two elements for which the relation between them can be derived from ...
141 views

### Computing and maintaining the minimum of a set $S$ of integers while allowing updates on $S$

This question is about computing and maintaining the minimum of a set $S$ of integers while allowing updates on $S$. The computation model we are considering is the unit-cost RAM machine with linear ...
92 views

412 views

### Sorting with an average of $\mathrm{lg}(n!)+o(n)$ comparisons

Is there a comparison-based sorting algorithm that uses an average of $\mathrm{lg}(n!)+o(n)$ comparisons? Existence of a worst-case $\mathrm{lg}(n!)+o(n)$ comparison algorithm is an open problem, but ...
74 views

### Lower bound for reversing a list using queues

How do you prove (or disprove) that a list of length $n$ cannot be reversed in time $o(n \log n)$ using $O(1)$ queues? Each queue is FIFO. Time refers to the number of operations on the queues. ...
461 views

### Sorting a programs instructions until it works

Lets say I have a computer program below. (define (factorial x) (if (= x 0) 1 (else (* x (factorial (- x 1))))) I then take each line of the ...
270 views

### Determining what can be achieved by a permutation of elements of a noncommutative group

Fix a finite group $G$. I am interested in the following decision problem: the input is some elements of $G$ with a partial order on them, and the question is whether there is a permutation of the ...
3k views

### Efficient recognition of sequences sortable by transpositions?

While reading the post, Probability of generating a desired permutation by random swaps, by Aaronson, I got interested in restricted sorting problem: If we restrict sorting algorithms to use ...
373 views

### Does any DAG can be topologically sorted? [closed]

I am not good enough in computer science. My intention is to solve some programming problem in terms of DAG's. The key point is that before getting them into database, I need run "topological sort" in ...
919 views

### Is sorting $n$ real numbers in time $O(n \sqrt{\log n})$ and linear space possible?

In the recent preprint https://arxiv.org/abs/1801.00776, it is claimed that $n$ real numbers can be sorted in time $$O(n \sqrt{\log n}),$$ and linear space. The paper seems reasonable, though I am ...
260 views

### How fast can we sort a list if we know how it was written?

Let $G$ be a linear time (deterministic) turing machine that takes positive integers $n$ in unary to lists of length $n.$ For any fixed such $G$, define sparse-sort(G,n) as the problem of sorting the ...
2k views

### Comparison-based data structure for finding items

Is there a data structure that takes an unordered array of $n$ items, performs preprocessing in $O(n)$ and answers queries: is there some element $x$ on the list, each query in worst time $O(\log n)$? ...
121 views

### Necessary and sufficient number of comparisons by every element to fully sort a set of n elements? [duplicate]

Given $n$ distinct elements. Is there a sorting algorithm which ensures that every element is compared atmost $\lg n$ time? Or is there a higher lower bound?
237 views

### Original reference for Huffman shaped Merge Sort?

What is the first publication of the concept of optimizing merge sort by identifying sequences of consecutive positions in increasing orders (aka runs) in linear time; then repeatedly merging the ...
Motivated by the question from this blog post, the following data structure question seems interesting and fun to me. Preprocess: A list of numbers $A = a_1,...,a_n$ Query(s,t,k): Return the $k$-th ...