Sufficient conditions for efficient indexing under different matchings

The most important task derived from the massive digital data accumulation in the world, is efficient access to this data, hence the importance of indexing. In the last decade, many different types of matching relations were defined, each requiring an efficient indexing scheme. Cole and Hariharan in a ground breaking paper [Cole and Hariharan, SIAM J. Comput., 33(1):26–42, 2003], formulate sufficient conditions for building an efficient indexing for quasi-suffix collections, collections that behave as suffixes. It was shown that known matchings, including parameterized, 2-D array and order preserving matchings, fit their indexing settings. In this paper, we formulate more basic sufficient conditions based on the order relation derived from the matching relation itself, our conditions are more general than the previously known conditions.