Succinct navigational oracles for families of intersection graphs on a circle
Acan, Huseyin; Chakraborty, Sankardeep; Jo, Seungbum; Nakashima, Kei; Sadakane, Kunihiko; Satti, Srinivasa Rao
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3045192Utgivelsesdato
2022Metadata
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Originalversjon
Theoretical Computer Science. 2022, 928 151-166. https://doi.org/10.1016/j.tcs.2022.06.022Sammendrag
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 circle graphs, k-polygon-circle graphs, circle-trapezoid graphs, 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 trapezoid graphs, and give a succinct navigational oracle for this class of graphs.