Volume 8 (2021): Edition 15 (November 2021)

Détails du magazine
Format
Magazine
eISSN
2182-1976
Première publication
16 Apr 2016
Période de publication
2 fois par an
Langues
Anglais

4 Articles
Accès libre

Bishop Independence on the Surface of a Square Prism

Publié en ligne: 07 Dec 2021
Pages: 1 - 12

Résumé

Bishop Independence concerns determining the maximum number of bishops that can be placed on a board such that no bishop can attack any other bishop. This paper presents the solution to the bishop independence problem, determining the bishop independence number, for all sizes of boards on the surface of a square prism.

• 05C69
• 00A08
Accès libre

Diameter-Separation of Chessboard Graphs

Publié en ligne: 07 Dec 2021
Pages: 13 - 26

Résumé

We define the queens (resp., rooks) diameter-separation number to be the minimum number of pawns for which some placement of those pawns on an n × n board produces a board with a queens graph (resp., rooks graph) with a desired diameter d. We determine these numbers for some small values of d.

Accès libre

Adjustable Coins

Publié en ligne: 07 Dec 2021
Pages: 27 - 39

Résumé

In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The user may run one algorithm at a time for the specified cost, or give up and pay the penalty. The probability of success may be implied by randomization in the algorithm, or by assuming a probability distribution on the input space, which lead to different variants of the problem. The goal is to minimize the expected cost of the process under the assumption that the algorithms are independent. We study several variants of this problem, and present possible solution strategies and a hardness result.

Accès libre

Who is Guilty?

Publié en ligne: 07 Dec 2021
Pages: 41 - 52

Résumé

We discuss a generalization of logic puzzles in which truth-tellers and liars are allowed to deviate from their pattern in case of one particular question: “Are you guilty?”