Recognizing Map Graphs of Bounded Treewidth

A map is a partition of the sphere into interior-disjoint regions homeomorphic to closed disks. Some regions are labeled as nations, while the remaining ones are labeled as holes. A map in which at most k nations touch at the same point is a k -map, while it is hole-free if it contains no holes. A g...

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Bibliographic Details
Published in:Algorithmica Vol. 86; no. 2; pp. 613 - 637
Main Authors: Angelini, Patrizio, Bekos, Michael A., Da Lozzo, Giordano, Gronemann, Martin, Montecchiani, Fabrizio, Tappini, Alessandra
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2024
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Apexes
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Graphs
Mathematics of Computing
Theory of Computation
Fixed-parameter tractability
Map graphs
K-map graphs
Treewidth
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:A map is a partition of the sphere into interior-disjoint regions homeomorphic to closed disks. Some regions are labeled as nations, while the remaining ones are labeled as holes. A map in which at most k nations touch at the same point is a k -map, while it is hole-free if it contains no holes. A graph is a map graph if there is a bijection between its vertices and the nations of a map, such that two nations touch if and only the corresponding vertices are connected by an edge. We present a fixed-parameter tractable algorithm for recognizing map graphs parameterized by treewidth. Its time complexity is linear in the size of the graph. It reports a certificate in the form of a so-called witness, if the input is a yes-instance. Our algorithmic framework is general enough to test, for any k , if the input graph admits a k -map or a hole-free  k -map.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-023-01180-6