Recent Advances in the Study of the Dandelion Code, Happy Code, and Blob Code Spanning Tree Representations

In 1999, Picciotto described three bijective tree codings: the Dandelion Code, the Happy Code, and the Blob Code. In this paper, we report three recent advances concerning these codings. First, we show that the Dandelion Code, the Happy Code, and the MHappy Code of Caminiti and Petreschi belong to a family of eight ´Dandelion-like´ codings. This family splits naturally into two groups of four codings, with the codings in each group having identical locality and heritability properties. Second, we describe linear-time encoding and decoding algorithms for the Blob Code, which supersede the usual quadratic-time algorithms. Finally, we adapt the codings to give bijective representations for the spanning trees of a complete bipartite graph.