On linear-time alphabet-independent 2-dimensional pattern matching

Abstract

We present a version of the alphabet-independent linear-time 2-dimensional pattern matching algorithm of Galil and Park (GP algorithm). The main part of GP algorithm is the construction of a so-called witness table. We develop a series of new tools that makes this construction easier to understand. Some properties of paths on lattices are considered. A useful concept of long duels is introduced, and applied to the 2D-matching problem. Special types of patterns with large monochromatic centers are introduced and investigated. One of the iterations in GP algorithm (related to radiant-periodic images) is removed. Other iterations are simplified, one due to the use of long duels, and the other due to the use of a simpler algorithm for the computation of witnesses for vectors lying on the same line. We give a simpler algorithm for the so-called suffix-testing problem, which is crucial in GP algorithm. As a consequence, our algorithm avoids the need for suffix trees (as well as their compacted versions) that are considered in GP algorithm.