Succinct Navigational Oracles for Families of Intersection Graphs on a Circle

Hüseyin Acan; Sankardeep Chakraborty; Seungbum Jo; Kei Nakashima; Kunihiko Sadakane; Srinivasa Rao Satti

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arXiv · 2010.04333

Succinct Navigational Oracles for Families of Intersection Graphs on a Circle

Hüseyin Acan·Sankardeep Chakraborty·Seungbum Jo·Kei Nakashima·Kunihiko Sadakane·Srinivasa Rao Satti

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Abstract

We consider the problem of designing succinct navigational oracles, i.e., succinct data structures supporting basic navigational queries such as degree, adjacency, and neighborhood efficiently for intersection graphs on a circle, which include graph classes such as {\it circle graphs}, {\it $k$-polygon-circle graphs}, {\it circle-trapezoid graphs}, {\it trapezoid graphs}. The degree query reports the number of incident edges to a given vertex, the adjacency query asks if there is an edge between two given vertices, and the neighborhood query enumerates all the neighbors of a given vertex. We first prove a general lower bound for these intersection graph classes and then present a uniform approach that lets us obtain matching lower and upper bounds for representing each of these graph classes. More specifically, our lower bound proofs use a unified technique to produce tight bounds for all these classes, and this is followed by our data structures which are also obtained from a unified representation method to achieve succinctness for each class. In addition, we prove a lower bound of space for representing {\it trapezoid} graphs and give a succinct navigational oracle for this class of graphs.

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Hüseyin Acan, Sankardeep Chakraborty, Seungbum Jo, Kei Nakashima, Kunihiko Sadakane, Srinivasa Rao Satti. 2020-10-09. Succinct Navigational Oracles for Families of Intersection Graphs on a Circle. https://arxiv.org/abs/2010.04333

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