Academic Journal
Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits.
| Τίτλος: | Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits. |
|---|---|
| Συγγραφείς: | Pettie, Seth, Ramachandran, Vijaya |
| Πηγή: | ACM Transactions on Algorithms; 2008, Vol. 4 Issue 1, p5:1-5:27, 27p, 1 Diagram, 5 Charts |
| Θεματικοί όροι: | Spanning trees, Algorithms, Linear systems, Tree graphs, Algebra |
| Περίληψη: | For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best-known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear, running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of input. In this article we develop some general methods for reducing exponentially the consumption of random bits in comparison-based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant, without affecting the expected running time. Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or O(1)-wise independent sampler. The prominent exception, and the main focus of this article, is a linear-time randomized minimum spanning tree algorithm that is not derived from the well-known Karger-Klein-Tarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on soft heaps. Further, using our algorithm as a guide, we present a unified view of the existing "nongreedy" minimum spanning tree algorithms. Concepts from the Karger-Klein-Tarjan algorithm, such as F-lightness,MSTverification, and sampled graphs, are related to the concepts of edge corruption, subgraph contractibility, and soft heaps, which are the basis of the deterministic MST algorithms of Chazelle and Pettie-Ramachandran. [ABSTRACT FROM AUTHOR] |
| Copyright of ACM Transactions on Algorithms is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 |
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| Header | DbId: edb DbLabel: Complementary Index An: 31662964 RelevancyScore: 833 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 833.189575195313 |
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| Items | – Name: Title Label: Title Group: Ti Data: Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pettie%2C+Seth%22">Pettie, Seth</searchLink><br /><searchLink fieldCode="AR" term="%22Ramachandran%2C+Vijaya%22">Ramachandran, Vijaya</searchLink> – Name: TitleSource Label: Source Group: Src Data: ACM Transactions on Algorithms; 2008, Vol. 4 Issue 1, p5:1-5:27, 27p, 1 Diagram, 5 Charts – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Spanning+trees%22">Spanning trees</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Tree+graphs%22">Tree graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best-known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear, running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of input. In this article we develop some general methods for reducing exponentially the consumption of random bits in comparison-based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant, without affecting the expected running time. Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or O(1)-wise independent sampler. The prominent exception, and the main focus of this article, is a linear-time randomized minimum spanning tree algorithm that is not derived from the well-known Karger-Klein-Tarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on soft heaps. Further, using our algorithm as a guide, we present a unified view of the existing "nongreedy" minimum spanning tree algorithms. Concepts from the Karger-Klein-Tarjan algorithm, such as F-lightness,MSTverification, and sampled graphs, are related to the concepts of edge corruption, subgraph contractibility, and soft heaps, which are the basis of the deterministic MST algorithms of Chazelle and Pettie-Ramachandran. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of ACM Transactions on Algorithms is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1145/1328911.1328916 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 5:1 Subjects: – SubjectFull: Spanning trees Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Linear systems Type: general – SubjectFull: Tree graphs Type: general – SubjectFull: Algebra Type: general Titles: – TitleFull: Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pettie, Seth – PersonEntity: Name: NameFull: Ramachandran, Vijaya IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: 2008 Type: published Y: 2008 Identifiers: – Type: issn-print Value: 15496325 Numbering: – Type: volume Value: 4 – Type: issue Value: 1 Titles: – TitleFull: ACM Transactions on Algorithms Type: main |
| ResultId | 1 |