2015
DOI: 10.1214/14-aap1041
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Jigsaw percolation: What social networks can collaboratively solve a puzzle?

Abstract: We introduce a new kind of percolation on finite graphs called jigsaw percolation. This model attempts to capture networks of people who innovate by merging ideas and who solve problems by piecing together solutions. Each person in a social network has a unique piece of a jigsaw puzzle. Acquainted people with compatible puzzle pieces merge their puzzle pieces. More generally, groups of people with merged puzzle pieces merge if the groups know one another and have a pair of compatible puzzle pieces. The social … Show more

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Cited by 25 publications
(43 citation statements)
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“…Definition 1. For i = 1, 2, let E i ⊂ [n] (2) be a set of pairs of elements of V := [n]. Let G be the ordered triple G := (V, E 1 , E 2 ); we call this object a double graph.…”
Section: Introductionmentioning
confidence: 99%
“…Definition 1. For i = 1, 2, let E i ⊂ [n] (2) be a set of pairs of elements of V := [n]. Let G be the ordered triple G := (V, E 1 , E 2 ); we call this object a double graph.…”
Section: Introductionmentioning
confidence: 99%
“…Artificial systems such as groups of robots behaving in a self organized manner show superior performance in solving their tasks, when they adopt algorithms inspired by the animal behaviors in groups [3][4][5][6]. Human groups such as organizational teams outperform the single individuals in a variety of tasks, including problem solving, innovative projects, and production issues [7][8][9][10][11].…”
Section: Introductionmentioning
confidence: 99%
“…The premise is that each of n people has a piece of a puzzle which must be combined in a certain way to solve the puzzle. Using the model, Brummit, Chatterjee, Dey, and Sivakoff [4] were able to show that some networks are better than others at solving certain puzzles, and that this is fundamentally due to the contrasting properties of the network. This motivates both a solid understanding of the jigsaw process and detailed knowledge of the social network in order to optimise performance and problem-solving.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…Brummitt, Chatterjee, Dey, and Sivakoff [4] studied the model when the red graph is the binomial random graph and with various deterministic possibilities for the blue graph, including a Hamilton cycle, or other connected graphs of bounded maximum degree, and provided upper and lower bounds for the percolation threshold probabilities.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%