Routing by matching on convex pieces of grid graphs
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| Názov: | Routing by matching on convex pieces of grid graphs |
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| Autori: | H. Alpert, R. Barnes, S. Bell, A. Mauro, N. Nevo, N. Tucker, H. Yang |
| Zdroj: | Computational Geometry. 104:101862 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Elsevier BV, 2022. |
| Rok vydania: | 2022 |
| Predmety: | Computational Geometry (cs.CG), FOS: Computer and information sciences, Extremal problems in graph theory, Distance in graphs, parallel sorting, makespan, 68U05 (05C85, 68M10), motion planning, Hypergraphs, 01 natural sciences, Trees, Polyhedra and polytopes, regular figures, division of spaces, token graph, FOS: Mathematics, Mathematics - Combinatorics, Computer Science - Computational Geometry, Combinatorics (math.CO), routing number, 0101 mathematics |
| Popis: | 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) has routing number rt(R) in O(w(R)+h(R)). We show that for the subgraph P of the infinite square lattice enclosed by any convex polygon, its routing number rt(P) is in O(w(P)+h(P)). 32 pages, 16 figures |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| Jazyk: | English |
| ISSN: | 0925-7721 |
| DOI: | 10.1016/j.comgeo.2022.101862 |
| DOI: | 10.48550/arxiv.2106.10751 |
| Prístupová URL adresa: | http://arxiv.org/abs/2106.10751 |
| Rights: | CC BY NC ND |
| Prístupové číslo: | edsair.doi.dedup.....3caab64a12d516b3e3ff565b537b7002 |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | 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) has routing number rt(R) in O(w(R)+h(R)). We show that for the subgraph P of the infinite square lattice enclosed by any convex polygon, its routing number rt(P) is in O(w(P)+h(P)).<br />32 pages, 16 figures |
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| ISSN: | 09257721 |
| DOI: | 10.1016/j.comgeo.2022.101862 |