For planar graphs, we propose a PTAS for Roman domination (and show that nothing better exists), and we get a constant approximation for win-win. Keep your data safe and secure with mSecure 5 If you have any questions or comments, please. Still the same is true if each idle server can move along one edge while the first of both requests is being served. Dont take any chances with your passwords and private information. We show that the same is true for Roman domination, the well studied problem variant that asks for each vertex to either possess its own server or to have a neighbor with two servers. A vertex is safe eternal m - secure if it is. For the problem of placing a minimum number of servers such that two requests at different nodes can be served with two different servers (called win-win), we present a logarithmic approximation, and we prove that nothing better is possible. that in response to an attack more than one guards can move to its adjacent locations to defend an attack. This paper studies domination problems for two requests.
For instance, when a request can occur at any node in a graph and requires a server at that node, a minimum dominating set represents a minimum set of servers that serve an arbitrary single request by moving a server along at most one edge.
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mSecure 5 Password Manager For Android, iOS, MAC and Windows 10 PC. We also find the safe eternal m - security number of some classes of graphs.ĭominating sets in their many variations model a wealth of optimization problems like facility location or distributed file sharing. Compare MSecure VS NordPass and find out whats different, what people are saying.
Safe eternal m - security number ( σ sm ) is the minimum cardinality of all safe eternal m - secure sets in a graph. In this paper we study some properties of safe eternal m - secure sets. A vertex is safe eternal m - secure if it is either adjacent to exactly one vertex in an eternal m - secure set or present in the set itself. An eternal m - secure set is defined in a similar way with only one exception that in response to an attack more than one guards can move to its adjacent locations to defend an attack. This situation can be interpreted as defending an attack at the place r i by moving a guard from v i to r i, where guards are deployed at the places, which are represented by the vertices in D i −1. The cardinality of a smallest eternal 1 - secure set in a graph G is called the eternal 1 - security number of G. An eternal 1-secure set, in a graph G = ( V, E ) is a set D ⊂ V having the property that for any finite sequence of vertices r 1, r 2 ,…, r k, there exists a sequence of vertices v 1, v 2 ,…, v k and a sequence D = D 0, D 1, D 2 ,…, D k of dominating sets of G, such that for each i, 1 ⩾ i ⩾ k, D i = ( D i -1 −, where v i ∈ D i −1, and r i ∈ N, where r i = v i is possible.
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