In the first part of the talk, we present a new approach in succinct representation of trees which unifies and enhances the power of pre-existing succinct representations of trees for various families of trees (such as ordered and k-ary trees).
In the second part of the talk, we discuss some related topics in succinct representations. We first sketch a dynamic version of our succinct representation of trees, where the encoded tree is changing by insertion and deletion of nodes. We conclude by exploring the topic of space lower bounds for succinct encodings.
This is joint work with J.Ian Munro, Rajeev Raman, and S.Srinivasa Rao.