Placing Labels in Road Maps: Algorithms and Complexity

• Published in: Algorithmica Vol. 82; no. 7; pp. 1881 - 1908
• Main Authors: Gemsa, Andreas, Niedermann, Benjamin, Nöllenburg, Martin
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2020; Springer Nature B.V
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Apexes; Cartography; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Labels; Mathematics of Computing; Theory of Computation; NP-hardness; Road maps; Efficient tree-based algorithm; Map labeling
• ISSN: 0178-4617; 1432-0541; 1432-0541
• DOI: 10.1007/s00453-020-00678-7

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 NP-hard in general, but the problem can be solved in O ( n 3 ) 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.