### 抜粋

Let P be an x-monotone orthogonal polygon with n vertices. We call P a simple histogram if its upper boundary is a single edge; and a double histogram if it has a horizontal chord from the left boundary to the right boundary. Two points p and q in P are co-visible if and only if the (axis-parallel) rectangle spanned by p and q completely lies in P. In the r-visibility graph G(P) of P, we connect two vertices of P with an edge if and only if they are co-visible. We consider routing with preprocessing in G(P). We may preprocess P to obtain a label and a routing table for each vertex of P. Then, we must be able to route a packet between any two vertices s and t of P, where each step may use only the label of the target node t, the routing table and the neighborhood of the current node, and the packet header. The routing problem has been studied extensively for general graphs, where truly compact and efficient routing schemes with polylogartihmic routing tables have turned out to be impossible. Thus, special graph classes are of interest. We present a routing scheme for double histograms that sends any data packet along a path of length at most twice the (unweighted) shortest path distance between the endpoints. The labels, routing tables, and headers need O(log n) bits. For the simple histograms, we obtain a routing scheme with optimal routing paths, O(log n)-bit labels, one-bit routing tables, and no headers.

元の言語 | English |
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ホスト出版物のタイトル | WALCOM |

ホスト出版物のサブタイトル | Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings |

編集者 | M. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung |

出版者 | Springer |

ページ | 43-54 |

ページ数 | 12 |

ISBN（印刷物） | 9783030398804 |

DOI | |

出版物ステータス | Published - 2020 1 1 |

イベント | 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore 継続期間: 2020 3 31 → 2020 4 2 |

### 出版物シリーズ

名前 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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巻 | 12049 LNCS |

ISSN（印刷物） | 0302-9743 |

ISSN（電子版） | 1611-3349 |

### Conference

Conference | 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 |
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国 | Singapore |

市 | Singapore |

期間 | 20/3/31 → 20/4/2 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## フィンガープリント Routing in histograms' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings*(pp. 43-54). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 12049 LNCS). Springer. https://doi.org/10.1007/978-3-030-39881-1_5