Testing Simon’s congruence asks whether two strings have the same set of subsequences of length no greater than a given integer. In the light of the recent discovery of an optimal linear algorithm for testing Simon’s congruence, we solve the Simon’s congruence pattern matching problem. The problem requires finding all substrings of a text that are congruent to a pattern under the Simon’s congruence. Our algorithm efficiently solves the problem in linear time in the length of the text by reusing results from previous computations with the help of new data structures called X-trees and Y-trees. Moreover, we define and solve variants of the Simon’s congruence pattern matching problem. They require finding the longest and shortest substring of the text as well as the shortest subsequence of the text which is congruent to the pattern under the Simon’s congruence. Two more variants which ask for the longest congruent subsequence of the text and optimizing the pattern matching problem are left as open problems.
|Title of host publication||33rd International Symposium on Algorithms and Computation, ISAAC 2022|
|Editors||Sang Won Bae, Heejin Park|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|Publication status||Published - 2022 Dec 1|
|Event||33rd International Symposium on Algorithms and Computation, ISAAC 2022 - Virtual, Online, Korea, Republic of|
Duration: 2022 Dec 19 → 2022 Dec 21
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||33rd International Symposium on Algorithms and Computation, ISAAC 2022|
|Country/Territory||Korea, Republic of|
|Period||22/12/19 → 22/12/21|
Bibliographical noteFunding Information:
Funding This research was supported by the NRF grant (NRF-2020R1A4A3079947) and the AI Graduate School Program (No. 2020-0-01361) funded by the Korea government (MSIT).
© Sungmin Kim, Sang-Ki Ko, and Yo-Sub Han.
All Science Journal Classification (ASJC) codes