A Short Note on Derandomization of Perfect Target Set Selection

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 293)


Consider the following process on a simple undirected connected graph \( {\text{G}}\left( {V,E} \right) \). At the beginning, only a set S of vertices are active. Subsequently, a vertex is activated if at least an \( \alpha \in \left( {0,1} \right) \) fraction of its neighbors are active. The process stops only when no more vertices can be activated. Following earlier papers, we call S an α perfect target set, abbreviated α-PTS, if all vertices are activated at the end. Chang [1] proposes a randomized polynomial-time algorithm for finding an α-PTS of expected size \( (2\sqrt 2 + 3)\left\lceil {\alpha |{\text{V}}|} \right\rceil \), where the expectation is taken over the random coin tosses of the algorithm. We note briefly that the method of conditional expectation can be used to derandomize Chang’s algorithm. So the derandomized algorithm finds an α-PTS of size no more than \( (2\sqrt 2 + 3)\left\lceil {\alpha |{\text{V}}|} \right\rceil \) given any simple undirected connected graph.


Target set selection Repetitive polling game Fault propagation Global cascade 



Ching-Lueh Chang is supported in part by the Ministry of Economic Affairs under grant 102-E0616 and the National Science Council under grant 101-2221-E-155-015-MY2.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Zen VoceHsinchu countyTaiwan, Republic of China
  2. 2.Department of Computer Science and EngineeringYuan-Ze UniversityTaoyuanTaiwan

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