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Make unit disk graph given set of points
Make unit disk graph given set of points











make unit disk graph given set of points

Graphs, such as interval graphs, trapezoid graphs, and circular arc graphs Agnarsson et al. The problem is polynomially solvable for some intersection Result, for any ϵ > 0, on bipartite graphs is NP-hard (this result Planar bipartite graphs of maximum degree 3 Eto et al. The distance- d independent set (D dIS) problem, for any fixed d ≥ 3, is known to be NP-hard for bipartite graphs Chang and Nemhauser ( 1984) and The objective of the minimum distance- d dominating set (MD dDS) problem is to find a D dDS of minimum cardinality in a given graph G. A D dDS for an integer d ≥ 1 in a simple unweighted graph G = ( V, E ) is defined as a set of vertices V ′ ⊆ V such that, for each vertex u ∈ V, either (i) u ∈ V ′, or (ii) v ∈ V ′ such that, the shortest path distance between u and v is at most d. We define a generalized version of MDS problem as distance- d dominating set (D dDS) problem. The objective of MDS problem is to find a dominating set of minimum cardinality in G. The dominating set of minimum cardinality in a graph G is called the minimum dominating set (MDS) of G. In a simple unweighted graph G = ( V, E ), dominating set is defined as a set of vertices V ′ ⊆ V such that for each vertex u ∈ V, either (i) u ∈ V ′, or (ii) there exist v ∈ V ′ such that v is a neighbor of u. In fact for d = 2, the D dIS problem and MIS problem are the same. Observe that the D dIS problem is a generalization of the MIS problem and Is called as maximum distance- d independent set (MD dIS). Given unweighted graph G, the objective of the maximum distance- d independent setĬardinality in G. Of G such that the shortest path distance (i.e., the number of edges on a shortest path)īetween every pair of vertices in I is at least d. Independent set (D dIS) of an unweighted graph G = ( V, E ) is an independent set I Unweighted graph G, and such a set is called as maximum independent The maximum independent set problemĪsks to find an independent set of maximum size in a given Vertices of G is known as an independent set of G.

make unit disk graph given set of points

Given an unweighted graph G = ( V, E ), a non-empty subset of pairwise non-adjacent













Make unit disk graph given set of points