Succinct Representation of Search Trees on Trees

Abstract: A search tree on trees (STT) is a data structure for performing a search for a target vertex in a reference tree. A standard binary search tree is a special case of an STT, where the reference tree is a path of totally ordered elements. In this paper, we study the problem of succinct representation of STTs. We consider two cases: (1) general search trees on trees, and (2) Steiner-closed search trees on trees [Bose et al. TALG 2023]. For both cases, we present representations that can be constructed in polynomial time and achieve optimal space up to the lower-order additive terms. We also present data structures for supporting fast traversals of both general and Steiner-closed STTs. For general STTs our data structure still takes optimal space up to lower-order additive terms.