Routing in histograms

Man Kwun Chiu, Jonas Cleve, Katharina Klost, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Max Willert

研究成果: Conference contribution


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.

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
出版ステータスPublished - 2020
イベント14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore
継続期間: 2020 3 312020 4 2


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


Conference14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)


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