Traversal with Enumeration of Geometric Graphs in Bounded Space
SAHAND KHAKABIMAMAGHANI, Masood Masjoody, LADISLAV STACHO · Journal of Interconnection Networks · 2019
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph G with the integer lattice, seen as a graph, in such a way that the resulting hypothetical graph can be traversed using a known algorithm which is based on face routing. To overcome the problem with hypothetical vertices and edges, we develop an algorithm for visiting any k-th neighborhood of a vertex in a graph straight-line drawn in the plane using O(k log k) memory. The memory needed to complete the traversal of a geometric graph then turns out to depend on the maximum graph distance among pairs of distinct vertices of G whose Euclidean distance is greater than one and less than [Formula: see text].