# 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} }

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

### Succinct Data Structure for Path Graphs

- Computer Science2022 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.

### Succinct Encodings for Families of Interval Graphs

- Computer Science, MathematicsAlgorithmica
- 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.

### Succinct Navigational Oracles for Families of Intersection Graphs on a Circle

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2022

### Indexing Graph Search Trees and Applications

- Computer Science, MathematicsMFCS
- 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…

### Succinct Encodings for Families of Interval Graphs

- Computer ScienceAlgorithmica
- 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.

### Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees

- Computer Science, MathematicsISAAC
- 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…

### Shorter Labeling Schemes for Planar Graphs

- Mathematics, Computer ScienceSODA
- 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 $n^{2+o(1)}$.

### Compact Representation of Graphs with Small Bandwidth and Treedepth

- Computer Science, Mathematics2020 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.

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

- Computer Science, MathematicsCOCOA
- 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.

### Breadth-First Rank/Select in Succinct Trees and Distance Oracles for Interval Graphs

- Computer ScienceArXiv
- 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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