Succinct Data Structures for Series-Parallel, Block-Cactus and 3-Leaf Power Graphs
Data Structures and Algorithms
2021-08-27 v2
Abstract
We design succinct encodings of {\it series-parallel, block-cactus} and {\it 3-leaf power} graphs while supporting the basic navigational queries such as degree, adjacency and neighborhood {\it optimally} in the RAM model with logarithmic word size. One salient feature of our representation is that it can achieve optimal space even though the exact space lower bound for these graph classes is not known. For these graph classes, we provide succinct data structures with optimal query support for the first time in the literature. For series-parallel multigraphs, our work also extends the works of Uno et al. (Disc. Math. Alg. and Appl., 2013) and Blelloch and Farzan (CPM, 2010) to produce optimal bounds.
Keywords
Cite
@article{arxiv.2108.10776,
title = {Succinct Data Structures for Series-Parallel, Block-Cactus and 3-Leaf Power Graphs},
author = {Sankardeep Chakraborty and Seungbum Jo and Kunihiko Sadakane and Srinivasa Rao Satti},
journal= {arXiv preprint arXiv:2108.10776},
year = {2021}
}