A Query-Efficient Quantum Algorithm for Maximum Matching on General Graphs
We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for bipartite graphs. In particular, for a graph with n vertices and m...
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| Published in | Algorithms and Data Structures Vol. 12808; pp. 543 - 555 |
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| Main Authors | , |
| Format | Book Chapter |
| Language | English |
| Published |
Switzerland
Springer International Publishing AG
2021
Springer International Publishing |
| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 3030835073 9783030835071 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-030-83508-8_39 |
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| Summary: | We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for bipartite graphs. In particular, for a graph with n vertices and m edges, our algorithm makes O(n7/4) $$O(n^{7/4})$$ queries in the matrix model and O(n3/4(m+n)1/2) $$O(n^{3/4}(m+n)^{1/2})$$ queries in the list model. Our approach combines Gabow’s classical maximum matching algorithm [Gabow, Fundamenta Informaticae, ’17] with the guessing tree method of Beigi and Taghavi [Beigi and Taghavi, Quantum, ’20]. |
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| Bibliography: | Original Abstract: We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for bipartite graphs. In particular, for a graph with n vertices and m edges, our algorithm makes O(n7/4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{7/4})$$\end{document} queries in the matrix model and O(n3/4(m+n)1/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{3/4}(m+n)^{1/2})$$\end{document} queries in the list model. Our approach combines Gabow’s classical maximum matching algorithm [Gabow, Fundamenta Informaticae, ’17] with the guessing tree method of Beigi and Taghavi [Beigi and Taghavi, Quantum, ’20]. |
| ISBN: | 3030835073 9783030835071 |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-030-83508-8_39 |