The folk solution and Boruvka’s algorithm in minimum cost spanning tree problems

Bergantiños, Gustavo; Vidal-Puga, Juan

doi:10.1016/j.dam.2011.04.017

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…It is the Equal Remaining Obligation solution (Feltkamp et al (1994)), the Potters-value (Branzei et al (2004)), the average of a number of population monotonic solutions introduced in Norde et al (2004), and it was given its name in . Several characterizations of this solution 1 have been provided, for example in Bergantinos and Vidal-Puga (2007), Bergantinos and Kar (2010), Bergantinos and Vidal-Puga (2011) and Branzei et al (2004). A central role in some of these characterizations is the axiom of population monotonicity (Sprumont (1990)) that guarantees dynamic stability: if a new agent joins then the other agents are not harmed.…”

Section: Introductionmentioning

confidence: 99%

The degree and cost adjusted folk solution for minimum cost spanning tree games

Norde

2019

Games and Economic Behavior

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In this paper two cost sharing solutions for minimum cost spanning tree problems are introduced, the degree adjusted folk solution and the cost adjusted folk solution. These solutions overcome the problem of the classical reductionist folk solution as they have considerable strict ranking power, without breaking established axioms. As such they provide affirmative answers to open questions, put forward in Bogomolnaia and Moulin (2010) and .

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Section: Introductionmentioning

confidence: 99%

The degree and cost adjusted folk solution for minimum cost spanning tree games

Norde

2019

Games and Economic Behavior

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“…For Adaptive HDBSCAN, the minimum spanning tree is built adaptively based on the number of points being clustered. For smaller numbers of points, Prim's algorithm [19] is used, whereas Boruvka's algorithm [20] is used for a larger number of data points.…”

Section: Adaptive Hdbscan Implementationmentioning

confidence: 99%

Adaptive Hierarchical Density-Based Spatial Clustering Algorithm for Streaming Applications

Vijayan

Aziz

2022

Telecom

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Clustering algorithms are commonly used in the mining of static data. Some examples include data mining for relationships between variables and data segmentation into components. The use of a clustering algorithm for real-time data is much less common. This is due to a variety of factors, including the algorithm’s high computation cost. In other words, the algorithm may be impractical for real-time or near-real-time implementation. Furthermore, clustering algorithms necessitate the tuning of hyperparameters in order to fit the dataset. In this paper, we approach clustering moving points using our proposed Adaptive Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm, which is an implementation of an adaptive approach to building the minimum spanning tree. We switch between the Boruvka and the Prim algorithms as a means to build the minimum spanning tree, which is one of the most expensive components of the HDBSCAN. The Adaptive HDBSCAN yields an improvement in execution time by 5.31% without depreciating the accuracy of the algorithm. The motivation for this research stems from the desire to cluster moving points on video. Cameras are used to monitor crowds and improve public safety. We can identify potential risks due to overcrowding and movements of groups of people by understanding the movements and flow of crowds. Surveillance equipment combined with deep learning algorithms can assist in addressing this issue by detecting people or objects, and the Adaptive HDBSCAN is used to cluster these items in real time to generate information about the clusters.

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Section: Introductionmentioning

confidence: 99%

The Degree and Cost Adjusted Folk Solution for Minimum Cost Spanning Tree Games

Norde

2013

SSRN Journal

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A minimum cost spanning tree problem analyzes how to eciently connect a group of individuals to a source. Once the ecient tree is obtained, the addressed question is how to allocate the total cost among the involved agents. One prominent solution in allocating this minimum cost is the so-called Folk solution. Unfortunately, in general, the Folk solution is not easy to compute. We identify a class of mcst problems in which the Folk solution is obtained in an easy way.

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The folk solution and Boruvka’s algorithm in minimum cost spanning tree problems

Abstract: a b s t r a c tBoruvka's algorithm, which computes a minimum cost spanning tree, is used to define a rule to share the cost among the nodes (agents). We show that this rule coincides with the folk solution, a very well-known rule of this literature.

Cited by 6 publications

References 12 publications

The degree and cost adjusted folk solution for minimum cost spanning tree games

The degree and cost adjusted folk solution for minimum cost spanning tree games

Adaptive Hierarchical Density-Based Spatial Clustering Algorithm for Streaming Applications

The Degree and Cost Adjusted Folk Solution for Minimum Cost Spanning Tree Games

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