Label Placement in Road Maps

TL;DR

This paper studies the problem of placing non-overlapping labels on road maps represented as graphs, proving NP-hardness in general but providing polynomial solutions for tree-structured maps.

Contribution

It establishes the computational complexity of label placement in road maps and offers efficient algorithms for tree-like road networks.

Findings

NP-hardness of label placement in general graphs

Polynomial-time solution for embedded trees

Enhanced understanding of map labeling complexity

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. We consider the 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 NP-hard in general, but the problem can be solved in polynomial time if the road map is an embedded tree.