Jeong Seop Sim

Linear-time construction of suffix arrays

The time complexity of suffix tree construction has been shown to be equivalent to that of sorting: O(n) for a constant-size alphabet or an integer alphabet and O(n log n) for a general alphabet. However, previous algorithms for constructing suffix arrays have the time complexity of O(n log n) even for a constant-size alphabet. In this paper we present a linear-time algorithm to construct suffix arrays for integer alphabets, which do not use suffix trees as intermediate data structures during its construction. Since the case of a constant-size alphabet can be subsumed in that of an integer alphabet, our result implies that the time complexity of directly constructing suffix arrays matches that of constructing suffix trees.

Constructing suffix arrays in linear time

Abstract The time complexity of suffix tree construction has been shown to be equivalent to that of sorting: O ( n ) for a constant-size alphabet or an integer alphabet and O ( n log n ) for a general alphabet. However, previous algorithms for constructing suffix arrays have the time complexity of O ( n log n ) even for a constant-size alphabet. In this paper we present a linear-time algorithm to construct suffix arrays for integer alphabets, which do not use suffix trees as intermediate data structures during its construction. Since the case of a constant-size alphabet can be subsumed in that of an integer alphabet, our result implies that the time complexity of directly constructing suffix arrays matches that of constructing suffix trees.

The consensus string problem for a metric is NP-complete

Given a set S of strings, a consensus string of S based on consensus error is a string w that minimizes the sum of the distances between w and all the strings in S. In this paper, we show that the problem of finding a consensus string based on consensus error is NP-complete when the penalty matrix is a metric.

Approximate periods of strings

The study of approximately periodic strings is relevant to diverse applications such as molecular biology, data compression, and computer-assisted music analysis. Here we study different forms of approximate periodicity under a variety of distance functions. We consider three related problems, for two of which we derive polynomial-time algorithms; we then show that the third problem is NP-complete.

A fast algorithm for order-preserving pattern matching

We present a new method of deciding the order-isomorphism between two strings.We show that the bad character rule can be applied to the OPPM problem.We present a space-efficient algorithm computing the shift table for text search.We present a linear-time algorithm for an integer alphabet in the worst case. Given a text T and a pattern P, the order-preserving pattern matching (OPPM) problem is to find all substrings in T which have the same relative orders as P. The OPPM has been studied in the fields of finding some patterns affected by relative orders, not by their absolute values. In this paper, we present a method of deciding the order-isomorphism between two strings even when there are same characters. Then, we show that the bad character rule of the Horspool algorithm for generic pattern matching problems can be applied to the OPPM problem and we present a space-efficient algorithm for computing shift tables for text search. Finally, we combine our bad character rule with the KMP-based algorithm to improve the worst-case running time. We give experimental results to show that our algorithm is about 2 to 6 times faster than the KMP-based algorithm in reasonable cases.

Fast Order-Preserving Pattern Matching

Given a text T and a pattern P, the order-preserving pattern matching (OPPM) problem is to find all substrings in T which have the same relative orders as P. The OPPM has been studied in the fields of finding some patterns affected by relative orders, not by their absolute values. For example, it can be applied to time series analysis like share prices on stock markets and to musical melody matching of two musical scores. In this paper, we present a new method of deciding the order-isomorphism between two strings even when there are same characters. Then, we show that the bad character rule of the Horspool algorithm for generic pattern matching problems can be applied to the OPPM problem. Finally, we present a fast algorithm for the OPPM problem and give experimental results to show that our algorithm is about 2 to 5 times faster than the KMP-based algorithm in reasonable cases.

Consensus Optimizing Both Distance Sum and Radius

The consensus string problem is finding a representative string (consensus) of a given set

Finding optimal alignment and consensus of circular strings

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Finding consensus and optimal alignment of circular strings

of strings. In this paper we deal with the consensus string problems optimizing both distance sum and radius, where the distance sum is the sum of (Hamming) distances from the strings in

Approximate Periods of Strings

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