In this paper, we study source location from a deterministic point of view by modeling it as the minimum cost doubly resolving set (DRS) problem, which is a strengthening of the well-known metric dimension problem.
In this paper, two similar NP-hard optimization problems on graphs are considered: the metric dimension problem and the problem of determining a doubly resolving set with the minimum cardinality.
Also, Central America became the first regional conflict of the Cold War era that the United States and the Soviet Union under Mikhail Gorbachev worked together to resolve, setting the stage for further breakthroughs in U.S.-Soviet relations.
In this paper, we consider the Johnson graphs J n,k) and Kneser graphs K n,k), and obtain various constructions of resolving sets for these graphs.
As well as general constructions, we show that various interesting combinatorial objects can be used to obtain resolving sets in these graphs, including (for Johnson graphs) projective planes and symmetric designs, as well as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems and toroidal grids.
The metric dimension μ is the smallest size of a resolving set for Γ.
A set of vertices S in a graph G is a resolving set for G if, for any two vertices u,v, there exists x∈S such that the distances d u,x ≠d v,x).
A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v.
"We can say that we are sorry and humbled only because we are resolved to set things right," said Zarges.
The Tinsley grievance, however it is resolved, could set a precedent for how N.B.A. teams deal with players who are bound by contract but no longer wanted.
