A bounded-error quantum polynomial-time algorithm for two graph bisection problems
Abstract 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-bisec...
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Gespeichert in:
| Autor*in: |
Younes, Ahmed [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Quantum information processing - Springer US, 2002, 14(2015), 9 vom: 14. Juli, Seite 3161-3177 |
|---|---|
| Übergeordnetes Werk: |
volume:14 ; year:2015 ; number:9 ; day:14 ; month:07 ; pages:3161-3177 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11128-015-1069-y |
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OLC207514754X |
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| 520 | |a Abstract 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 $$O(m^2)$$ for a graph with m edges and in the worst case runs in $$O(n^4)$$ 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 $$1-\epsilon $$ for small $$\epsilon >0$$ using a polynomial space resources. | ||
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a bounded-error quantum polynomial-time algorithm for two graph bisection problems |
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A bounded-error quantum polynomial-time algorithm for two graph bisection problems |
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Abstract 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 $$O(m^2)$$ for a graph with m edges and in the worst case runs in $$O(n^4)$$ 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 $$1-\epsilon $$ for small $$\epsilon >0$$ using a polynomial space resources. © Springer Science+Business Media New York 2015 |
| abstractGer |
Abstract 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 $$O(m^2)$$ for a graph with m edges and in the worst case runs in $$O(n^4)$$ 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 $$1-\epsilon $$ for small $$\epsilon >0$$ using a polynomial space resources. © Springer Science+Business Media New York 2015 |
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Abstract 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 $$O(m^2)$$ for a graph with m edges and in the worst case runs in $$O(n^4)$$ 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 $$1-\epsilon $$ for small $$\epsilon >0$$ using a polynomial space resources. © Springer Science+Business Media New York 2015 |
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A bounded-error quantum polynomial-time algorithm for two graph bisection problems |
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https://doi.org/10.1007/s11128-015-1069-y |
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