Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, March 19, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Ahad N. Zehmakan

Tight Bounds on the Minimum Size of a Dynamo

Consider a graph G and an initial coloring, where each node is black or white. In each round, all nodes simultaneously update their color based on a predefined rule. In a threshold model, a node becomes black if a certain fraction/number of its neighbors are black, and white otherwise. We say a node set D is a dynamo whenever the following holds: If D is fully black initially, the whole graph becomes black eventually. In this talk, we prove tight upper and lower bounds on the minimum size of a dynamo. Moreover, some hardness results regarding the problem of determining the minimum size of a dynamo for a given graph G are presented.

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