Related papers: The Query Complexity of a Permutation-Based Varian…

In this paper we study noisy sorting without re-sampling. In this problem there is an unknown order $a_{\pi(1)} < ... < a_{\pi(n)}$ where $\pi$ is a permutation on $n$ elements. The input is the status of $n \choose 2$ queries of the form…

We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a $n \times n$ grid is labeled with an ordering constraint -- ascending (A) or descending (D) -- and the…

Permutation patterns and pattern avoidance are central, well-studied concepts in combinatorics and computer science. Given two permutations $\tau$ and $\pi$, the pattern matching problem (PPM) asks whether $\tau$ contains $\pi$. This…

We close the gap in the proof (published by Chen and Lin) of formulas for the minimum number of questions required in the expected case for Mastermind and its variant called AB game, where both games are played with two pegs and $n$ colors.…

We prove that the problem of reconstructing a permutation $\pi_1,\dotsc,\pi_n$ of the integers $[1\dotso n]$ given the absolute differences $|\pi_{i+1}-\pi_i|$, $i = 1,\dotsc,n-1$ is NP-complete. As an intermediate step we first prove the…

A tournament is a complete directed graph. It is well known that every tournament contains at least one vertex v such that every other vertex is reachable from v by a path of length at most 2. All such vertices v are called *kings* of the…

We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…

Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural…

We determine sharp bounds on the price of bandit feedback for several variants of the mistake-bound model. The first part of the paper presents bounds on the $r$-input weak reinforcement model and the $r$-input delayed, ambiguous…

A sequence $f\colon\{1,\dots,n\}\to\mathbb{R}$ contains a permutation $\pi$ of length $k$ if there exist $i_1<\dots<i_k$ such that, for all $x,y$, $f(i_x)<f(i_y)$ if and only if $\pi(x)<\pi(y)$; otherwise, $f$ is said to be $\pi$-free. In…

Sampling permutations from S_n is a fundamental problem from probability theory. The nearest neighbor transposition chain \cal{M}}_{nn} is known to converge in time \Theta(n^3 \log n) in the uniform case and time \Theta(n^2) in the constant…

In this article, we describe an algorithm to determine whether a permutation class C given by a finite basis B of excluded patterns contains a finite number of simple permutations. This is a continuation of the work initiated in [Brignall,…

The "pancake problem" asks how many prefix reversals are sufficient to sort any permutation $\pi \in \mathcal{S}_k$ to the identity. We write $f(k)$ to denote this quantity. The best known bounds are that $\frac{15}{14}k -O(1) \le f(k)\le…

String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…

We consider the problem where P is an unknown permutation on {0,1,...,2^n - 1}, y is an element of {0,1,...,2^n - 1}, and the goal is to determine the minimum r > 0 such that P^r(y) = y (where P^r is P composed with itself r times).…

This paper presents a novel class of information-theoretic strategies for solving the game of Mastermind, achieving state-of-the-art performance among known heuristic methods. The core contribution is the application of a weighted entropy…

The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by…

Consider a game of permutation wordle in which a player attempts to guess a secret permutation of length $n$ in as few guesses as possible. In each round, the guessing player is told which indices of their guessed permutation are correct.…

Multiparty computation is raising importance because it's primary objective is to replace any trusted third party in the distributed computation. This work presents two multiparty shuffling protocols where each party, possesses a private…

We introduce an extension of Mastermind called Clear Mastermind with enhanced feedback inspired by that from Wordle. The only difference between Clear Mastermind and Mastermind is a rule that provides more precise feedback, as found in…