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V. Paschos (2013)
Paradigms of combinatorial optimization : problems and new approaches
RJ Lipton, R Tarjan (1980)
Applications of a planar separator theoremSIAM J. Comput., 9
D. Delling, Daniel Fleischman, A. Goldberg, Ilya Razenshteyn, Renato Werneck (2014)
An exact combinatorial algorithm for minimum graph bisectionMathematical Programming, 153
B. Hendrickson, R. Leland (1995)
An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel ComputationsSIAM J. Sci. Comput., 16
Matthias Hein, Thomas Bühler (2010)
An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCAArXiv, abs/1012.0774
A. Younes, J. Rowe, J. Miller (2004)
Enhanced quantum searching via entanglement and partial diffusionPhysica D: Nonlinear Phenomena, 237
A. Younes (2013)
Towards More Reliable Fixed Phase Quantum Search AlgorithmApplied Mathematics & Information Sciences, 7
J. Díaz, M. Kaminski (2006)
MAX-CUT and MAX-BISECTION are NP-hard on unit disk graphsTheor. Comput. Sci., 377
M. Garey, David Johnson, L. Stockmeyer (1976)
Some Simplified NP-Complete Graph ProblemsTheor. Comput. Sci., 1
(2009)
A new diffusion-basedmultilevel algorithm for computing graph partitions
P. Sanders, Christian Schulz (2013)
Think Locally, Act Globally: Highly Balanced Graph Partitioning
A. Land, A. Doig (1960)
An Automatic Method for Solving Discrete Programming Problems
S. Bhatt, F. Leighton (1983)
A Framework for Solving VLSI Graph Layout ProblemsJ. Comput. Syst. Sci., 28
P. Høyer (2000)
Arbitrary phases in quantum amplitude amplificationPhysical Review A, 62
D. Delling, A. Goldberg, Ilya Razenshteyn, Renato Werneck (2011)
Graph Partitioning with Natural Cuts2011 IEEE International Parallel & Distributed Processing Symposium
T. Rivlin (1974)
The Chebyshev polynomials
P. Sanders, Christian Schulz (2011)
Distributed Evolutionary Graph PartitioningArXiv, abs/1110.0477
R. Lipton, R. Tarjan (1977)
Applications of a planar separator theorem18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
Jianbo Shi, J. Malik (1997)
Normalized cuts and image segmentationProceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition
J Shi, J Malik (2000)
Normalized cuts and image segmentationIEEE Trans. Pattern Anal. Mach. Intell., 22
William Hager, D. Phan, Hongchao Zhang (2009)
An exact algorithm for graph partitioningMathematical Programming, 137
Lov Grover (1997)
Quantum Mechanics Helps in Searching for a Needle in a HaystackPhysical Review Letters, 79
V. Guruswami, Yury Makarychev, P. Raghavendra, David Steurer, Yuan Zhou (2011)
Finding Almost-Perfect Graph Bisections
Harald Räcke (2008)
Optimal hierarchical decompositions for congestion minimization in networksProceedings of the fortieth annual ACM symposium on Theory of computing
G. Malewicz, Matthew Austern, Aart Bik, James Dehnert, I. Horn, Naty Leiser, G. Czajkowski (2010)
Pregel: a system for large-scale graph processingProceedings of the 2010 ACM SIGMOD International Conference on Management of data
D. Delling, Renato Werneck (2013)
Faster Customization of Road Networks
M. Armbruster (2007)
Branch-and-Cut for a Semidefinite Relaxation of Large-scale Minimum Bisection Problems
MR Garey, DS Johnson (1979)
Computers and Intractability. A Guide to the Theory of NP-Completeness
Zi Xu, D. Du, Dachuan Xu (2014)
Improved approximation algorithms for the max-bisection and the disjoint 2-catalog segmentation problemsJournal of Combinatorial Optimization, 27
Ellis Johnson, A. Mehrotra, G. Nemhauser (1993)
Min-cut clusteringMathematical Programming, 62
A. Feldmann, P. Widmayer (2011)
An O(n^4) time algorithm to compute the bisection width of solid grid graphsCTIT technical reports series, 730
U. Feige, M. Langberg (2001)
The RPR2 rounding technique for semidefinite programsJ. Algorithms, 60
David Johnson, W. Freeman
The Np-completeness Column: an Ongoing Guide Garey and Myself in Our Book ''computers and Intractability: a Guide to the Theory of Np-completeness,''
U Feige, M Langberg (2006)
The RPR $$^2$$ 2 rounding technique for semidefinite programsJ. Algorithms, 60
P. Raghavendra, Ning Tan (2011)
Approximating CSPs with global cardinality constraints using SDP hierarchies
C. Bazgan, Marek Karpinski (2005)
On the Complexity of Global Constraint Satisfaction
(2003)
Graph cut textures: image and video synthesis using graph cuts
M. Armbruster, Marzena Fügenschuh, C. Helmberg, Alexander Martin (2008)
A Comparative Study of Linear and Semidefinite Branch-and-Cut Methods for Solving the Minimum Graph Bisection Problem
K. Jansen, Marek Karpinski, A. Lingas, Eike Seidel (2001)
Polynomial Time Approximation Schemes for MAX-BISECTION on Planar and Geometric GraphsSIAM J. Comput., 35
The aim of the paper was to propose a bounded-error quantum polynomial-time algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a graph with even number of vertices, the aim of the max-bisection problem is to divide the vertices into two subsets of the same size to maximize the number of edges between the two subsets, while the aim of the min-bisection problem is to minimize the number of edges between the two subsets. The proposed algorithm runs in $$O(m^2)$$ O ( m 2 ) for a graph with m edges and in the worst case runs in $$O(n^4)$$ O ( n 4 ) for a dense graph with n vertices. The proposed algorithm targets a general graph by representing both problems as Boolean constraint satisfaction problems where the set of satisfied constraints are simultaneously maximized/minimized using a novel iterative partial negation and partial measurement technique. The algorithm is shown to achieve an arbitrary high probability of success of $$1-\epsilon $$ 1 - ϵ for small $$\epsilon >0$$ ϵ > 0 using a polynomial space resources.
Quantum Information Processing – Springer Journals
Published: Jul 14, 2015
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