Local Algorithms for Estimating Effective Resistance Article Swipe
Pan Peng
,
Daniel Lopatta
,
Yuichi Yoshida
,
Gramoz Goranci
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2106.03476
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2106.03476
Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of the effective resistances, we still lack efficient algorithms to exactly compute or approximate them on massive graphs. In this work, we design several \emph{local algorithms} for estimating effective resistances, which are algorithms that only read a small portion of the input while still having provable performance guarantees. To illustrate, our main algorithm approximates the effective resistance between any vertex pair $s,t$ with an arbitrarily small additive error $\varepsilon$ in time $O(\mathrm{poly}(\log n/\varepsilon))$, whenever the underlying graph has bounded mixing time. We perform an extensive empirical study on several benchmark datasets, validating the performance of our algorithms.
Related Topics
Concepts
Bounded function
Benchmark (surveying)
Cluster analysis
Metric (unit)
Computer science
Algorithm
Vertex (graph theory)
Graph
Clustering coefficient
Reliability (semiconductor)
Mathematics
Theoretical computer science
Discrete mathematics
Machine learning
Operations management
Mathematical analysis
Physics
Geodesy
Quantum mechanics
Power (physics)
Economics
Geography
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2106.03476
- https://arxiv.org/pdf/2106.03476
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3168557774
All OpenAlex metadata
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https://openalex.org/W3168557774Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2106.03476Digital Object Identifier
- Title
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Local Algorithms for Estimating Effective ResistanceWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2021Year of publication
- Publication date
-
2021-06-07Full publication date if available
- Authors
-
Pan Peng, Daniel Lopatta, Yuichi Yoshida, Gramoz GoranciList of authors in order
- Landing page
-
https://arxiv.org/abs/2106.03476Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2106.03476Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2106.03476Direct OA link when available
- Concepts
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Bounded function, Benchmark (surveying), Cluster analysis, Metric (unit), Computer science, Algorithm, Vertex (graph theory), Graph, Clustering coefficient, Reliability (semiconductor), Mathematics, Theoretical computer science, Discrete mathematics, Machine learning, Operations management, Mathematical analysis, Physics, Geodesy, Quantum mechanics, Power (physics), Economics, GeographyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.benchmark | 124 |
| abstract_inverted_index.datasets, | 125 |
| abstract_inverted_index.effective | 37, 63, 90 |
| abstract_inverted_index.efficient | 42 |
| abstract_inverted_index.empirical | 120 |
| abstract_inverted_index.extensive | 119 |
| abstract_inverted_index.important | 4 |
| abstract_inverted_index.algorithms | 43, 67 |
| abstract_inverted_index.estimating | 62 |
| abstract_inverted_index.importance | 34 |
| abstract_inverted_index.resistance | 1, 91 |
| abstract_inverted_index.similarity | 9 |
| abstract_inverted_index.underlying | 110 |
| abstract_inverted_index.validating | 126 |
| abstract_inverted_index.\emph{local | 59 |
| abstract_inverted_index.algorithms. | 131 |
| abstract_inverted_index.algorithms} | 60 |
| abstract_inverted_index.approximate | 48 |
| abstract_inverted_index.arbitrarily | 99 |
| abstract_inverted_index.clustering, | 22 |
| abstract_inverted_index.guarantees. | 82 |
| abstract_inverted_index.illustrate, | 84 |
| abstract_inverted_index.performance | 81, 128 |
| abstract_inverted_index.applications | 19 |
| abstract_inverted_index.approximates | 88 |
| abstract_inverted_index.reliability, | 27 |
| abstract_inverted_index.resistances, | 38, 64 |
| abstract_inverted_index.$\varepsilon$ | 103 |
| abstract_inverted_index.recommendation | 23 |
| abstract_inverted_index.n/\varepsilon))$, | 107 |
| abstract_inverted_index.$O(\mathrm{poly}(\log | 106 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |