Dynamic Compact Planar Embeddings

This paper presents a way to compactly represent dynamic connected planar embeddings, which may contain self loops and multi-edges, in 4m + o(m) bits, to support basic navigation in O(lg n) time and edge and vertex insertion and deletion in O(lg(1+epsilon) n) time, where n and m are respectively the number of vertices and edges currently in the graph and epsilon is an arbitrary positive constant. Previous works on dynamic succinct planar graphs either consider decremental settings only or are restricted to triangulations where the outer face must be a simple polygon and all inner faces must be triangles. To the best of our knowledge, this paper presents the first representation of dynamic compact connected planar embeddings that supports a full set of dynamic operations without restrictions on the sizes or shapes of the faces.