Abstract—Wireless sensor networks need very efficient network protocols due to the sensors’ limited communication and computation capabilities. Network planarization – find...
Let > 0 be a constant. For any edge-weighted planar graph G and a subset S of nodes of G, there is a subgraph H of G of weight a constant times that of the minimum Steiner tree...
We show that computing the lexicographically first four-coloring for planar graphs is p 2hard. This result optimally improves upon a result of Khuller and Vazirani who prove this ...
For a graph G and a collection of vertex pairs {(s1, t1), . . . , (sk, tk)}, the k disjoint paths problem is to find k vertex-disjoint paths P1, . . . , Pk, where Pi is a path fr...
A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum weight triangulation (MWT) problem, we are looking for a triangula...