Space-Economical Construction of Index Structures for All Suffixes of a String

The minimum all-suffixes directed acyclic word graph (MASDAWG) of a string w has |w| + 1 initial nodes, where the dag induced by all reachable nodes from the k-th initial node conforms with the DAWG of the k-th suffix of w. A new space-economical algorithm for the construction of MASDAWG(w) is presented. The algorithm reads a given string w from right to left, and constructs MASDAWG(w) without suffix links. It performs in time linear in the output size. Furthermore, we introduce the minimum all-suffixes compact DAWG (MASCDAWG). CDAWGs are known to be more space-economical than DAWGs, and thus MASCDAWG(w) requires smaller space than MASDAWG(w). We present an on-line (right-to-left) algorithm to build MASCDAWG(w) without suffix links, whose running time is also linear in its size.