Succinct Representation of Labeled Graphs

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Abstract

In many applications, the properties of an object being modeled are stored as labels on vertices or edges of a graph. In this paper, we consider succinct representation of labeled graphs. Our main results are the succinct representations of labeled and multi-labeled graphs (we consider vertex labeled planar triangulations, as well as edge labeled planar graphs and the more general k-page graphs) to support various label queries efficiently. The additional space cost to store the labels is essentially the information-theoretic minimum. As far as we know, our representations are the first succinct representations of labeled graphs. We also have two preliminary results to achieve the main results. First, we design a succinct representation of unlabeled planar triangulations to support the rank/select of edges in ccw (counter clockwise) order in addition to the other operations supported in previous work. Second, we design a succinct representation for a k-page graph when k is large to support various navigational operations more efficiently. In particular, we can test the adjacency of two vertices in \(O(\lg k\lg\lg k)\) time, while previous work uses O(k) time (10; 14).