# Routing in histograms

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

## Abstract

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.

Original language English Proc. 14th International Conference and Workshops on Algorithms and Computation (WALCOM) M. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung Springer Gabler 43-54 12 9783030398804 https://doi.org/10.1007/978-3-030-39881-1_5 Published - 2020 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, SingaporeDuration: 31 Mar 2020 → 2 Apr 2020

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 12049 LNCS 0302-9743 1611-3349

### Conference

Conference 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 Singapore Singapore 31/03/20 → 2/04/20

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