A practical succinct data structure for tree-like graphs

Abstract

We present a new succinct data structure for graphs that are “tree-like,” in the sense that the number of “additional” edges (w.r.t. a spanning tree) is not too high. Our algorithmic idea is to represent a BFS-spanning tree of the graph with a succinct data structure for trees, and enhance it with additional information that accounts for the nontree edges. In practical tests, our data structure performs well for graphs containing up to 10% of non-tree edges, reducing the space of a pointerbased representation by a factor of ≈20, while increasing the worst-case running times for the operations by roughly the same factor.