The property suffix tree with dynamic properties

In the Property Indexing Problem the goal is to preprocess a text T of size n over a constant sized alphabet Σ and a set of intervals π over the text positions, such that given a query pattern P of size m we can report all of the occurrences of P in T which are completely contained within some interval from π. This type of matching is extremely helpful for scenarios in molecular biology where it has long been a practice to consider special areas in the genome by their structure. It is also helpful for solving pattern matching problems over weighted sequences.So far the focus has been on the static version of this problem where the intervals are given a priori and never changed. This paper focuses on several dynamic settings of π including an incremental version where new intervals are inserted into π, a decremental version where intervals are deleted from π, a fully dynamic version where intervals may be inserted into or deleted from π, and a batched insertions version where sets of intervals are inserted into π. In particular, the batched version provides a new (optimal) algorithm for the static case.