Routing by matching on convex pieces of grid graphs

The routing number is a graph invariant introduced by Alon, Chung, and Graham in 1994, and it has been studied for trees and other classes of graphs such as hypercubes. It gives the minimum number of routing steps needed to sort a set of distinct tokens, placed one on each vertex, where each routing...

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Bibliographic Details
Published in:Computational geometry : theory and applications Vol. 104; p. 101862
Main Authors: Alpert, H., Barnes, R., Bell, S., Mauro, A., Nevo, N., Tucker, N., Yang, H.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2022
Subjects:
Makespan
Motion planning
Parallel sorting
Routing number
Token graph
Motion planning
Makespan
Token graph
Parallel sorting
Routing number
ISSN:0925-7721
Online Access:Get full text
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Summary:The routing number is a graph invariant introduced by Alon, Chung, and Graham in 1994, and it has been studied for trees and other classes of graphs such as hypercubes. It gives the minimum number of routing steps needed to sort a set of distinct tokens, placed one on each vertex, where each routing step swaps a set of disjoint pairs of adjacent tokens. Our main theorem generalizes the known estimate that a rectangular grid graph R with width w(R) and height h(R) satisfies rt(R)∈O(w(R)+h(R)). We show that for the subgraph P of the infinite square lattice enclosed by any convex polygon, we have rt(P)∈O(w(P)+h(P)).
ISSN:0925-7721
DOI:10.1016/j.comgeo.2022.101862