A fast and lightweight filter-based algorithm for circular pattern matching

Abstract

Exact Circular Pattern Matching (ECPM) problem consists in finding all occurrences of the rotations of a pattern P of length m in a text T of length n. In this paper we present a fast filter-based algorithm for this problem.

SimpLiFiCPM: A Simple and Lightweight Filter-Based Algorithm for Circular Pattern Matching

“…Table 2 reports the elapsed time and speed-up comparisons for various pattern sizes (500 โ‰ค m โ‰ค 3000). As can be seen from Table 2 , Filter-CPM [ 8 ] runs faster than ACSMF-SimpleZero k in all cases. And in fact Filter-CPM [ 8 ] achieves a minimum of twofold speed-up for all the pattern sizes.…”

“…We have conducted our experiments on a PowerEdge R820 rack serve PC with 6-core Intel Xeon processor E5-4600 product family and 64โ€‰GB of RAM under GNU/Linux. With the help of the library used in [ 4 ], we have compared the running time of our preliminary work in [ 8 ] (referred to as Filter-CPM henceforth), ACSMF-SimpleZero k of [ 4 ], and SimpLiFiCPM. Table 2 reports the elapsed time and speed-up comparisons for various pattern sizes (500 โ‰ค m โ‰ค 3000).…”

“…At this point a brief discussion with respect to our preliminary work in [ 8 ] is in order. To reduce the text ๐’ฏ , we also employed six filters in [ 8 ].…”

“…At this point a brief discussion with respect to our preliminary work in [ 8 ] is in order. To reduce the text ๐’ฏ , we also employed six filters in [ 8 ]. While Filter 1 and Filter 4 remain identical, in SimpLiFiCPM, we have changed and improved Filters 2, 3, 5, and 6 to get better results.…”

Circular Pattern Matching with k Mismatches

“…In many real-world applications, such as in bioinformatics [4,22,25,7] or in image processing [3,33,34,32], any cyclic shift (rotation) of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P , if this distance is no more than k. This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers [17,8,6,5,9,24] have thus been devoted to solving the k-CPM problem but, to the best of our knowledge, only average-case upper bounds are known; i.e. in these works the assumption is that text T is uniformly random.…”