Walking Through Waypoints

• Published in: Algorithmica Vol. 82; no. 7; pp. 1784 - 1812
• Main Authors: Akhoondian Amiri, Saeed, Foerster, Klaus-Tycho, Schmid, Stefan
• 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; Combinatorial analysis; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Graphs; Mathematics of Computing; Polynomials; Theory of Computation; Walking; Waypoints; Networks; hardness; Algorithms; Distributed systems; Routing; Virtualization; Disjoint paths; Walks
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-020-00672-z

We initiate the study of a fundamental combinatorial problem: Given a capacitated graph  G = ( V , E ) , find a shortest walk (“route”) from a source  s ∈ V to a destination  t ∈ V that includes all vertices specified by a set  W P ⊆ V : the waypoints . This W aypoint R outing P roblem finds immediate applications in the context of modern networked systems. Our main contribution is an exact polynomial-time algorithm for graphs of bounded treewidth. We also show that if the number of waypoints is logarithmically bounded, exact polynomial-time algorithms exist even for general graphs. Our two algorithms provide an almost complete characterization of what can be solved exactly in polynomial time: we show that more general problems (e.g., on grid graphs of maximum degree 3, with slightly more waypoints) are computationally intractable.