Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the...
We present a polynomial-time approximation scheme (PTAS) for the Steiner tree problem with polygonal obstacles in the plane with running time O(n log2 n), where n denotes the numb...
In the Euclidean group Traveling Salesman Problem (TSP), we are given a set of points P in the plane and a set of m connected regions, each containing at least one point of P. We w...
Khaled M. Elbassioni, Aleksei V. Fishkin, Nabil H....
We show that for every set S of n points in the plane and a designated point rt ∈ S, there exists a tree T that has small maximum degree, depth and weight. Moreover, for every po...
The result of simulation of an idealized thin wet film connecting fixed points in the Euclidean plane is a length-minimizing curve. Gradually increasing the exterior pressure we ar...