Constructing the suffix tree of a tree with a large alphabet

Abstract

The problem of constructing the suffix tree of a common suffix tree (CS-tree) is a generalization of the problem of constructing the suffix tree of a string. It has many applications, such as in minimizing the size of sequential transducers and in tree pattern matching. The best-known algorithm for this problem is Breslauer's O(nlog|Σ|) time algorithm where n is the size of the CS-tree and |Σ| is the alphabet size, which requires O(n log n) time if |Σ| is large. We improve this bound by giving an O(n log log n) algorithm for integer alphabets. For trees called shallow k-ary trees, we give an optimal linear time algorithm. We also describe a new data structure, the Bsuffix tree, which enables efficient query for patterns of completely balanced k-ary trees from a k-ary tree or forest. We also propose an optimal O(n) algorithm for constructing the Bsuffix tree for integer alphabets.