Counting Power Domination Sets in Complete m-ary Trees
Sviatlana Kniahnitskaya, Michele Ortiz, Olivia Ramirez, Katharine, Shultis, Hays Whitlatch
TL;DR
This paper develops a recursive method to count power domination sets in complete m-ary trees, enabling efficient calculation of the probability of successful monitoring with randomly placed monitors.
Contribution
It introduces a recursive formula for counting power domination sets in complete m-ary trees, facilitating probability computation in exponential time with linear exponent.
Findings
Recursive formula for counting power domination sets
Probability computation in exponential time with linear exponent
Application to monitor placement success probability
Abstract
Motivated by the question of computing the probability of successful power domination by placing k monitors uniformly at random, in this paper we give a recursive formula to count the number of power domination sets of size k in a labeled complete m-ary tree. As a corollary we show that the desired probability can be computed in exponential with linear exponent time.
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Taxonomy
TopicsGame Theory and Applications