• QUANTUM ALGORITHMS FOR THE TRI...

Treffer: QUANTUM ALGORITHMS FOR THE TRIANGLE PROBLEM

Title:
QUANTUM ALGORITHMS FOR THE TRIANGLE PROBLEM
Authors:
MAGNIEZ, Frédéric, SANTHA, Miklos, SZEGEDY, Mario
Source:
SIAM journal on computing (Print). 37(2):413-424
Publisher Information:
Philadelphia, PA: Society for Industrial and Applied Mathematics, 2008.
Publication Year:
2008
Physical Description:
print, 32 ref
Original Material:
INIST-CNRS
Subject Terms:
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, 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, Recherche information. Graphe, Information retrieval. Graph, Divers, Miscellaneous, Calcul automatique, Computing, Cálculo automático, Complexité, Complexity, Complejidad, Concept, Concepto, Conception, Design, Diseño, Informatique, Computer science, Informática, Noeud, Node, Nudo, Ordinateur, Computer, Computadora, Requête, Query, Pregunta documental, Sous programme, Subroutine, Subprograma, 05Bxx, 68R10, 68Wxx, 68XX, Algorithme combinatoire, Combinatorial algorithm, Triangle, 05C85, 68W99, quantum algorithm, quanturn walk, query complexity, triangle problem
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
CNRS-LRI, UMR 8623 Université Paris-Sud, 91405 Orsay, France
Department of Computer Science, Rutgers University, Piscataway, NJ 08854, United States
ISSN:
0097-5397
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=20249011
Rights:
Copyright 2008 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
Accession Number:
edscal.20249011
Database:
PASCAL Archive

Weitere Informationen

We present two new quantum algorithms that either find a triangle (a copy of K3) in an undirected graph G on n nodes, or reject if G is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes ? (n10/7) queries. The second algorithm uses ? (n13/10) queries and is based on a design concept of Ambainis [in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004, pp. 22-31] that incorporates the benefits of quantum walks into Grover Search [L. Grover, in Proceedings of the Twenty-Eighth ACM Symposium on Theory of Computing, 1996, pp. 212-219]. The first algorithm uses only O(log n) qubits in its quantum subroutines, whereas the second one uses O(n) qubits. The Triangle Problem was first treated in [H. Buhrman et al., SIAM J. Comput., 34 (2005), pp. 1324-1330], where an algorithm with O(n + √nm) query complexity was presented, where m is the number of edges of G.