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9
votes
1answer
72 views

Encoding sets of permutations with a generating set and a set of excluded elements

Polynomial-time algorithms are known for finding generating sets of permutation groups, which is interesting since we can then represent those groups succinctly without giving up on polynomial-time ...
13
votes
0answers
284 views

$NP$-completeness of recognizing the difference of two permutations

Shor stated, in his comment to anonymous moose's answer to this question Can you identify the sum of two permutations in polynomial time?, that it is $NP$-complete to identify the difference of two ...
5
votes
0answers
82 views

Permutation optimization problem

Here is the problem as posed by Jerrum: "The computational complexity of the following problem is investigated: Given a permutation group specified as a set of generators, and a single target ...
4
votes
1answer
68 views

Compatible partial permutations

Please, correct my terminology as I am not a combinatorician (I am using http://en.wikipedia.org/wiki/Partial_permutation). Please, refer me to the solution if this is a solved problem. Let $P_k$ ...
0
votes
0answers
58 views

“Partial” invert a one-way permutation

First of all, to my best understanding, traditionally, if $f$ is a one-way function that maps a length $l$ bit string to another length $l$ bit string (i.e., $f:\{0,1\}^l\rightarrow\{0,1\}^l$), then ...
2
votes
1answer
72 views

Effect of constraints Density on the hardness of Betweness problem

Betweeness problem is well known NP-complete permutation problem. Given a family $M$ of triples $(a_i, a_j, a_k)$, the problem is to decide whether a permutation $\Phi$ of elements $a_1, a_2, ..., ...
-1
votes
1answer
44 views

Algorithm for calculating substitution combination with ordering

I need to calculate the combinations of elements with a substitution element. For example for elements [A,B] if the substitution is X the results should be ...
10
votes
1answer
933 views

Efficient algorithm for existence of permutation with differences sequence?

This question is motivated by this post, Can you identify the sum of two permutations in polynomial time? , and my interest in computational properties of permutations. A differences sequence $a_1, ...
2
votes
2answers
146 views

Finding the identity with permutation chains

I have the following problem: I'm given a list of size $K$ of random integer permutations of $[1..n]$, named $P_1$ to $P_K$, and an additional random permutation $Q$. How hard is to find a sequence ...
24
votes
2answers
1k views

Can you identify the sum of two permutations in polynomial time?

There were two questions asked recently on cs.se which were either related to or had a special case equivalent to the following question: Suppose you have a sequence $a_1, a_2, \ldots a_n$ of $n$ ...
-3
votes
1answer
86 views

the product of a matrix and a permutation matrix [closed]

Can a permutation matrix (P) be used to change the rank of another matrix (M)? Is there any literature to this effect, or to the contrary? I've tried a few small examples and the resulting matrix ...
3
votes
2answers
135 views

Sort with random deviations

I'm looking for an algorithm that will take a sorted array of numbers and generate a random permutation of this array in such a way that the probability of finding a larger element earlier in a ...
2
votes
1answer
131 views

Computing unique subset intersections

Given a set S = {si : {zj : z ∈ N} }, what is a time-efficient algorithm for computing the unique sets of intersections of all of the subsets of S? As per @JeffE's comment below, there are edge ...
2
votes
0answers
114 views

Complexity of the standardization

Let $(A, \leq)$ be a totally ordered alphabet. The standardization ${\tt std}(u)$ of a word $u \in A^n$ is the unique permutation of $n$ elements having the same inversions as $u$ (recall that an ...
17
votes
1answer
407 views

Asymptotically, how many permutations of $[1..n]$ have at most $k$ inversions?

Consider a permutation $\sigma$ of $[1..n]$. An inversion is defined as a pair $(i, j)$ of indices such that $i < j$ and $\sigma(i) > \sigma(j)$. Define $A_k$ to be the number of permutations ...
8
votes
2answers
241 views

Is there an efficient algorithm to find the i-th dearrangement?

Here is the background for this question. Friends and I were playing a game where everyone needs to give another people some gift. In order to determine who should give gift to whom, we decide to drew ...
7
votes
1answer
374 views

Efficiently finding the minimum number of transpositions needed to sort a list

I'd like an efficient method for calculating the minimum number of transpositions needed to sort a list. I don't need to know what the transpositions actually are. For example, the list [1, 1, 2, 0] ...
30
votes
12answers
1k views

Applications of representation theory of the symmetric group

Inspired by this question and in particular the final paragraph of Or's answer, I have the following question: Do you know of any applications of the representation theory of the symmetric group ...
21
votes
1answer
448 views

Deciding whether an NC${}^0_3$ circuit computes a permutation or not

I would like to ask about a special case of the question “Deciding if a given NC0 circuit computes a permutation” by QiCheng that has been left unanswered. A Boolean circuit is called an NC0k circuit ...
12
votes
1answer
285 views

Two matrices related by a permutation $B = P A P^T$ - complexity

What is computational complexity of the following problem: given two complex $n\times n$ matrices $A$ and $B$ check if there is a permutation matrix $P$ such that: $$B = P A P^T.$$ If it helps, one ...
5
votes
1answer
407 views

Number of permutations which have the same Kendall-Tau distance

Input: The number of elements $m$ and an (positive) integer distance $d$. Ouput: The number of permutations of $m$ elements which have Kendall-Tau distance $d$ from a fixed permutation. I think there ...
7
votes
1answer
479 views

How to shuffle colour balls?

I have 400 balls, in which 100 are red, 40 are yellow, 50 are green, 60 are blue, 70 are purple, 80 are black. (balls of the same colour are identical) i need an efficient shuffling algorithm, so ...
7
votes
4answers
398 views

How to shuffle cards with restrictions?

I want as uniformly as possible to pick from all full shuffles such that this additional criterion applied. For example, i would like to shuffle 4 decks of cards, and make sure: Any consecutive 4 ...
25
votes
1answer
558 views

Deciding if a given $\mathsf{NC}^0$ circuit computes a permutation

What is the complexity of deciding whether an $\mathsf{NC}^0$ circuit with $n$ input bits and $n$ output bits computes a permutation of $\{0,1\}^n$? in the other words, whether every bit strings in ...
1
vote
1answer
234 views

finding permutations which fulfills given conditions

Let $K$ be an ordered finite set. Consider some function $g:K^2 \rightarrow R$ such that $g(k1,k1') + g(k2,k2') \ge g(k1,k2') + g(k2,k1')$ where $k1 > k2$ (in order A1) and ...
9
votes
3answers
371 views

Permutation pattern matching in strings

Loosely speaking, permutation pattern matching deals with problems of the following kind: Given permutations $\pi$ in $S_n$ and $\sigma$ in $S_m$, with $m\leq n$, does $\pi$ contain a subsequence ...
2
votes
1answer
143 views

List the $k$-faces of an $n$-dimensional simplex

Suppose you are given an $n$-dimensional simplex S = [ 0 1 ... n ] which for the time being we think of as an ascending array of numbers from $0$ to $n$. Given ...
6
votes
0answers
147 views

Lowerbounds for in-situ permutation

What is the best known lowerbound for the worst case complexity of in-situ permutation (also called in-place rearrangement)? Has there been any reported progress after the 1970's article by Knuth ...
5
votes
2answers
408 views

Choosing random permutations in “strict” polynomial time

This question compares "strict" polynomial time, as opposed to "expected" polynomial time. Let $S = {1,2,…,n}$, and let $O$ be an ordering on elements of $S$. (The number of orderings is $n!$.) A ...
22
votes
4answers
1k views

Complexity of applying a permutation in-place

To my surprise, I was not able to find papers about this - probably searched the wrong keywords. So, we've got an array of anything, and a function $f$ on its indices; $f$ is a permutation. How do ...
3
votes
2answers
908 views

Counting length-k increasing subsequences in a permutation

(Originally posted on Math.SE.) Let $f$ be a permutation on $n$ letters. I want to count the number of $k$-long increasing subsequences quickly. One approach is to first use divide and conquer to ...
13
votes
2answers
511 views

Set Cover for Permutation Matrices

Given a set S of nxn permutation matrices (which is only a small fraction of the n! possible permutation matrices), how can we find minimal-size subsets T of S such that adding the matrices of T has ...
0
votes
1answer
481 views

How to compute ROOK Polynomials for NxM Matrices [closed]

How to compute ROOK Polynomials for NxM Matrices for k objects ?
6
votes
0answers
140 views

Constraint Satisfaction Problem: Choosing real numbers with variance in a certain range

I have a set of n real numbers. I want to repeatedly choose subsets of k elements such that the variance of these k numbers falls within some specified range, r = [l, u]. Moreover I want to do this ...
13
votes
6answers
856 views

Complexity of the Fisher-Yates Shuffle Algorithm

This question is in regard to the Fisher-Yates algorithm for returning a random shuffle of a given array. The Wikipedia page says that its complexity is O(n), but I think that it is O(n log n). In ...