Corpus ID: 237940627

Product Throttling

@inproceedings{Anderson2020ProductT,
  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},
  year={2020}
}
  • 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

References

SHOWING 1-10 OF 32 REFERENCES
Throttling for zero forcing and variants
TLDR
A new universal definition of throttling for variants of zero forcing and the study of throttleling for the minor monotone floor of zero forced graphs are introduced. Expand
Throttling for the game of Cops and Robbers on graphs
TLDR
This work considers trees, unicyclic graphs, incidence graphs of finite projective planes (a Meyniel extremal family of graphs), a family of cop-win graphs with maximum capture time, grids, and hypercubes, and obtains upper bounds on the cop-throttling number for families of graphs. Expand
Throttling zero force propagation speed on graphs
TLDR
This note looks at what happens when the size of the initial set of vertices colored black and the number of steps, called speed of propagaion, that it takes for all vertices to be colored black, and gives a tight relationship between the zero forcing number and theNumber of edges in the graph. Expand
Throttling positive semidefinite zero forcing propagation time on graphs
TLDR
A tight lower bound is established on the positive semidefinite throttling number of the graph as a function of the order, maximum degree, and positive semidescendent zero forcing number. Expand
Cops and robber on grids and tori
TLDR
This paper treats the classical cops and robber problem on a graph in function of any number k of cops, giving efficient algorithms for grids and tori and computing lower and upper bounds on the capture time. Expand
The capture time of a graph
TLDR
This work considers the game of Cops and Robbers played on finite and countably infinite connected graphs, and considers the ratio of the capture time to the number of vertices, and extends this notion of capture time density to infinite graphs. Expand
Optimizing the trade-off between number of cops and capture time in Cops and Robbers
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
TLDR
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
The Game of Overprescribed Cops and Robbers Played on Graphs
TLDR
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
TLDR
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
...
1
2
3
4
...