Placing Labels in Road Maps: Algorithms and Complexity
Andreas Gemsa, Benjamin Niedermann, Martin Nöllenburg · Algorithmica · 2020
Abstract A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. In this paper, we consider the computational cartographic problem to place non-overlapping road labels along the edges so that as many road sections as possible are identified by their name, i.e., covered by a label. We show that this is -hard in general, but the problem can be solved in $$O(n^3)$$ O(n3) time if the road map is an embedded tree with n vertices and constant maximum degree. This special case is not only of theoretical interest, but our algorithm in fact provides a very useful subroutine in exact or heuristic algorithms for labeling general road maps.