An Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game

Jacobs, Donald J.; Hendrickson, Bruce

doi:10.1006/jcph.1997.5809

Cited by 321 publications

(279 citation statements)

References 22 publications

(41 reference statements)

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“…In this case, algorithms such as [25] may be applied by dividing the global network into small globally rigid sub-components [31] (clusters) to reduce overall complexity. Each cluster computes its relative localization using some optimization technique.…”

Section: Global/distributed Optimization For Localizationmentioning

confidence: 99%

A Theory of Network Localization

Aspnes

Eren

Goldenberg

et al. 2006

IEEE Trans. on Mobile Comput.

563

396

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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks.We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.

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Section: Global/distributed Optimization For Localizationmentioning

confidence: 99%

A Theory of Network Localization

Aspnes

Eren

Goldenberg

et al. 2006

IEEE Trans. on Mobile Comput.

563

396

View full text Add to dashboard Cite

show abstract

“…They model the strength of the connection within the protein based on the 3-D Pebble Game [17], where the pebbles represent the degrees of freedom.…”

Section: Literature On Pebble Motionmentioning

confidence: 99%

Multi-Color Pebble Motion on Graphs

Goraly

Hassin

2009

Algorithmica

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We consider a graph with n vertices, and p < n pebbles of m colors. A pebble move consists of transferring a pebble from its current host vertex to an adjacent unoccupied vertex. The problem is to move the pebbles to a given new color arrangement.We study the feasibility version of the problem -does a given instance have a solution? We use an algorithm of [6] for the problem where each pebble has a distinct color to give a linear time algorithm for the feasibility decision problem on a general graph.

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“…Maxwell's rule for determining the stiffness of a structure is discussed and, as the authors mention, Maxwell realized this is only a necessary condition for a structure to be stiff. The exact condition is nontrivial to determine, but in a 2D structure xvi Foreword one can play the "pebble game" to resolve the question [3]. Maxwell's counting rule has been generalized for periodic lattices [4].…”

Section: To Ananya and Krishna To Alaa And Ismailmentioning

confidence: 99%

Front Matter

2017

Dynamics of Lattice Materials

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An Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game

Cited by 321 publications

References 22 publications

A Theory of Network Localization

A Theory of Network Localization

Multi-Color Pebble Motion on Graphs

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