Succinct Data Structures for SP, Block-Cactus and 3 -Leaf Power Graphs

Abstract

We design succinct encodings of series-parallel, block-cactus and 3-leaf power graphs while supporting the basic navigational queries such as degree, adjacency and neighborhood 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.