Corpus ID: 237940627

Product Throttling

  title={Product Throttling},
  author={Sarah E. Anderson and Karen L. Collins and Daniela Ferrero and Leslie Hogben and Carolyn Mayer and Ann N. Trenk and Shanise Walker},
  • Sarah E. Anderson, Karen L. Collins, +4 authors Shanise Walker
  • Published 23 December 2020
  • Mathematics
Throttling addresses the question of minimizing the sum or the product of the resources used to accomplish a task and the time needed to complete that task for various graph searching processes. Graph parameters of interest include various types of zero forcing, power domination, and Cops and Robbers. The resources used to accomplish a task can be blue vertices in zero forcing, Phasor Measurement Units (PMUs) in power domination, or cops in Cops and Robbers. The time is the number of rounds… Expand


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The capture time of a graph
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The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of roundsExpand
Capture on Grids and Tori with Different Numbers of Cops
This paper is a contribution to the classical cops and robber problem on a graph directed to two-dimensional grids and tori, and introduces the concept of work \(w_k=k\cdot t_k\) of an algorithm and study a possible speed-up using larger teams of cops. Expand
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This work considers the effect on the length of the game of Cops and Robbers when more cops are added to the game play, and gives the full range of capture times for any number of cops on trees, and the capture time for an asymptotic number of policemen on grids, hypercubes, and binomial random graphs. Expand
Domination in Graphs Applied to Electric Power Networks
It is shown that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs and a linear algorithm is given to solve the PDS for trees. Expand