Succinct Permutation Graphs

We present a succinct data structure for permutation graphs, and their superclass of circular i.e., structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022), our also supports distance shortest-path queries, as well adjacency neighborhood all in time. particular the first exact oracle (circular) graphs. A second degree queries time independent neighborhood's size at expense an $O(\log n/\log \log n)$-factor overhead running times. Furthermore, we develop class bipartite demonstrate how run algorithms directly over representations several problems graphs: Clique, Coloring, Independent Set, Hamiltonian Cycle, All-Pair Shortest Paths, others. Finally, initiate study semi-distributed graph representations; concept that smoothly interpolates between distributed (labeling schemes) centralized (standard structures). show turn some into by storing only $O(n)$ bits additional global information, circumventing bound labeling schemes