Lecture Notes in Computer Science 7659

Given ∈ [0, 1), the -Relative Error Periodic Pattern Problem (REPP) is the following: INPUT: An n-long sequence S of numbers si ∈ N in increasing order. OUTPUT: The longest -relative error periodic pattern, i.e., the longest subsequence si1 , si2 , . . . , sik of S, for which there exists a number p such that the absolute difference between any two consecutive numbers in the subsequence is at least p and at most p(1 + ). The best known algorithm for this problem has O(n) time complexity. This bound is too high for large inputs in practice. In this paper we give a new algorithm for finding the longest -relative error periodic pattern (the REPP problem). Our method is based on a transformation Partly supported by NSF grant CCR-09-04581, ISF grant 347/09, and BSF grant 2008217. Partly supported by BSF grant 2008217. Partly supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 347/09, Yahoo, Grant No. 2008217 from the United StatesIsrael Binational Science Foundation (BSF) and DFG. † Partly supported by ISF grant 347/09. G. Even and D. Rawitz (Eds.): MedAlg 2012, LNCS 7659, pp. 1–12, 2012. c © Springer-Verlag Berlin Heidelberg 2012