A note on updating suffix tree labels

Abstract

We investigate the problem of maintaining the arc labels in the suffix tree data structure [15] when it undergoes string insertions and deletions. In current literature, this problem is solved either by a simple accounting strategy to obtain amortized bounds [10, 18] or by a periodical suffix tree reconstruction to obtain worst-case bounds (according to the global rebuilding technique in [20]). Unfortunately, the former approach is simple and space-efficient at the cost of attaining amortized bounds for the single update; the latter is space-consuming in practice because it needs to keep two extra suffix tree copies. In this paper, we obtain a surprisingly simple real-time algorithm that achieves worst-case bounds and only requires small additional space (i.e., a bi-directional pointer per suffix tree arc). We analyze the problem by introducing a combinatorial coloring problem on the suffix tree arcs.