# Succinct Data Structures for Families of Interval Graphs

@inproceedings{Acan2019SuccinctDS,
title={Succinct Data Structures for Families of Interval Graphs},
author={H{\"u}seyin Acan and Sankardeep Chakraborty and Seungbum Jo and S. Srinivasa Rao},
booktitle={Workshop on Algorithms and Data Structures},
year={2019}
}
• Published in
Workshop on Algorithms and…
25 February 2019
• Computer Science, Mathematics
We consider the problem of designing succinct data structures for interval graphs with $n$ vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time in the $\Theta(\log n)$-bit word RAM model. The degree query reports the number of incident edges to a given vertex in constant time, the adjacency query returns true if there is an edge between two vertices in constant time, the neighborhood query reports the set of all adjacent vertices in time…
12 Citations
• Computer Science
2022 Data Compression Conference (DCC)
• 2022
This work considers the problem of designing a succinct data structure for path graphs with n vertices while supporting degree, adjacency, and neighborhood queries efficiently, and provides two solutions that permits a simple and efficient implementation at the expense of more space.
• Computer Science, Mathematics
Algorithmica
• 2020
This work designs succinct data structures for interval graphs with n vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time, and extends these ideas to other variants of interval graphs, for example, proper/unit intervals, k-improper intervals, and circular-arc graphs.
• Computer Science, Mathematics
MFCS
• 2019
We consider the problem of compactly representing the Depth First Search (DFS) tree of a given undirected or directed graph having $n$ vertices and $m$ edges while supporting various DFS related
• Computer Science
Algorithmica
• 2020
This work designs succinct data structures for interval graphs with n vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time and extends these ideas to other variants of interval graphs, for example, proper/unit interval graphs.
• Computer Science, Mathematics
ISAAC
• 2020
We present the first succinct distance oracles for (unweighted) interval graphs and related classes of graphs, using a novel succinct data structure for ordinal trees that supports the mapping
• Mathematics, Computer Science
SODA
• 2020
This work designs a labeling scheme with labels of bit length that generalizes to graphs of bounded Euler genus with the same label length up to a second-order term, improving the previous best upper bound of $n^{2+o(1)}$.
• Shahin Kamali
• Computer Science, Mathematics
2020 Data Compression Conference (DCC)
• 2020
A lower bound is presented that certifies the oracle is succinct for certain values of k ∊ o(n) for graphs of bandwidth k and size n.
• Computer Science, Mathematics
COCOA
• 2021
This work designs 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 to provide succinct data structures with optimal query support for the first time in the literature.
• Computer Science
ArXiv
• 2020
We present the first succinct data structure for ordinal trees that supports the mapping between the preorder (i.e., depth-first) ranks and level-order (breadth-first) ranks of nodes in constant

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