On the Succinct Representation of Equivalence Classes

El-Zein, Hicham; Lewenstein, Moshe; Munro, J. Ian; Raman, Venkatesh; Chan, Timothy M.

doi:10.1007/s00453-016-0192-1

“…Finally, for the case when G ∈ C is not connected, we extend the above idea as follows. We first encode all the connected components of G separately, and encoding the sizes of the connected components using the encoding of [10,26] using at most O( √ n) additional bits. This implies we can still encode G in succinct space even if G is not connected.…”

Section: Graph Representation Using Tree Coveringmentioning

confidence: 99%

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

Chakraborty

¹

,

Jo

²

,

Sadakane

³

et al. 2023

Int. J. Found. Comput. Sci.

0

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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.

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“…Finally, for the case when G ∈ C is not connected, we extend the above idea as follows. We first encode all the connected components of G separately, and encoding the sizes of the connected components using the encoding of [9,25] using at most O( √ n) additional bits. This implies we can still encode G in succinct space even if G is not connected.…”

Section: Graph Representation Using Tree Coveringmentioning

confidence: 99%

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

Chakraborty¹,

Jo²,

Sadakane³

et al. 2021

Preprint

0

View full text Add to dashboard Cite

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.

show abstract