New problem results: Consecutive Block Minimization - Couverture souple

Layouni, Zoubir

Couverture souple

ISBN 10 : 6208992176 ISBN 13 : 9786208992170

Editeur : Our Knowledge Publishing, 2025

Synopsis

In this book, we focus on a special property in a binary matrix, known as the "1-consecutive property". A consecutive block is a sequence of consecutively located 1s. The problem is to find a permutation of the columns so that the number of consecutive blocks in the induced matrix is minimal. We point out that it is NP-complete for general instances, then we present applications to it, variants and a state of the art. Our first contribution consists in proving that CBM is NP-complete even when the binary matrix has only two 1's per row, by polynomially transforming the maximum-weight Hamiltonian chain problem to CBM restricted to the instances in question.A second contribution consisted in solving the question: is CBM approximable with guarantee? The answer was found in the form of a polynomial heuristic that constructs permutations leading to a number of consecutive blocks within 50% of the optimum.

Détails de l'édition

• Éditeur: Our Knowledge Publishing
• Date d'édition: 2025
• Langue: anglais
• ISBN 10: 6208992176
• ISBN 13: 9786208992170
• Reliure: Broché
• Nombre de pages: 52
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible