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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Veröffentlicht in:Computational geometry : theory and applications Jg. 104; S. 101862
Hauptverfasser: Alpert, H., Barnes, R., Bell, S., Mauro, A., Nevo, N., Tucker, N., Yang, H.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.06.2022
Schlagworte:
Makespan
Motion planning
Parallel sorting
Routing number
Token graph
Motion planning
Makespan
Token graph
Parallel sorting
Routing number
ISSN:0925-7721
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Abstract 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)).
AbstractList 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)).
ArticleNumber 101862
Author Alpert, H.
Yang, H.
Bell, S.
Mauro, A.
Nevo, N.
Tucker, N.
Barnes, R.
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  surname: Yang
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  email: hannay@mit.edu
  organization: MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, United States of America
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Cites_doi 10.4171/054
10.1090/S0273-0979-08-01238-X
10.1007/s41468-019-00043-w
10.1137/S0895480192236628
10.1093/imrn/rnt012
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Keywords Motion planning
Makespan
Token graph
Parallel sorting
Routing number
Language English
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StartPage 101862
SubjectTerms Makespan
Motion planning
Parallel sorting
Routing number
Token graph
Title Routing by matching on convex pieces of grid graphs
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