2-limited broadcast domination on grid graphs

Show simple item record

dc.contributor.author Slobodin, Aaron
dc.date.accessioned 2021-07-29T20:45:38Z
dc.date.available 2021-07-29T20:45:38Z
dc.date.copyright 2021 en_US
dc.date.issued 2021-07-29
dc.identifier.uri http://hdl.handle.net/1828/13190
dc.description.abstract Suppose there is a transmitter located at each vertex of a graph G. A k-limited broadcast on G is an assignment of the integers 0,1,...,k to the vertices of G. The integer assigned to the vertex x represents the strength of the broadcast from x, where strength 0 means the transmitter at x is not broadcasting. A broadcast of positive strength s from x is heard by all vertices at distance at most s from x. A k-limited broadcast is called dominating if every vertex assigned 0 is within distance d of a vertex whose transmitter is broadcasting with strength at least d. The k-limited broadcast domination number of G is the minimum possible value of the sum of the strengths of the broadcasts in a k-limited dominating broadcast of G. We establish upper and lower bounds for the 2-limited broadcast domination number of various grid graphs, in particular the Cartesian products of two paths, a path and a cycle, and two cycles. The upper bounds are derived by explicit broadcast constructions for these graphs. The lower bounds are obtained via linear programming duality by finding lower bounds for the fractional 2-limited multipacking number of these graphs. Finally, we present an algorithm to improve the lower bound for the 2-limited broadcast domination number of special sub-families of grids. We conclude this thesis with suggested open problems in broadcast domination and multipackings. en_US
dc.language English eng
dc.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.subject graph theory en_US
dc.subject broadcast domination en_US
dc.subject k-limited broadcast domination en_US
dc.subject multipacking en_US
dc.subject fractional 2-limited multipacking en_US
dc.subject optimization en_US
dc.subject discrete math en_US
dc.subject limited broadcast domination en_US
dc.subject limited multipacking en_US
dc.subject linear programming en_US
dc.title 2-limited broadcast domination on grid graphs en_US
dc.type Thesis en_US
dc.contributor.supervisor MacGillivray, Gary
dc.contributor.supervisor Ruskey, Frank
dc.degree.department Department of Mathematics and Statistics en_US
dc.degree.level Master of Science M.Sc. en_US
dc.description.scholarlevel Graduate en_US

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search UVicSpace


My Account