Result: The complexity of maximum matroid-greedoid intersection and weighted greedoid maximization
Title:
The complexity of maximum matroid-greedoid intersection and weighted greedoid maximization
Authors:
Source:
Efficient algorithmsDiscrete applied mathematics. 154(4):684-691
Publisher Information:
Amsterdam; Lausanne; New York, NY: Elsevier, 2006.
Publication Year:
2006
Physical Description:
print, 8 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Plans d'expériences et configurations, Designs and configurations, Géométrie, Geometry, Géométrie convexe et discrète, Convex and discrete geometry, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Approximation numérique, Numerical approximation, Aproximación numérica, Complexité, Complexity, Complejidad, Informatique théorique, Computer theory, Informática teórica, Intersection, Intersección, Matroïde, Matroid, Matroide, Maximisation, Maximization, Maximización, Optimisation combinatoire, Combinatorial optimization, Optimización combinatoria, Problème NP difficile, NP hard problem, Problema NP duro, Temps polynomial, Polynomial time, Tiempo polinomial, Forme normale conjonctive, Formule booléenne, Inapproximabilité, Inapproximability, Intractabilité, Satisfiabilité, Fixed-parameter intractability, NP-hardness
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Science, P.O. Box 68, University of Helsinki, 00014, Finland
ISSN:
0166-218X
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Mathematics
Mathematics
Accession Number:
edscal.17554865
Database:
PASCAL Archive
Further Information
The maximum intersection problem for a matroid and a greedoid, given by polynomial-time oracles, is shown NP-hard by expressing the satisfiability of boolean formulas in 3-conjunctive normal form as such an intersection. The corresponding approximation problems are shown NP-hard for certain approximation performance bounds. Moreover, some natural parameterized variants of the problem are shown W[P]-hard. The results are in contrast with the maximum matroid-matroid intersection which is solvable in polynomial time by an old result of Edmonds. We also prove that it is NP-hard to approximate the weighted greedoid maximization within 2nO(I) where n is the size of the domain of the greedoid.