Journal of KIISE (정보과학회 논문지)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Parallel Algorithms for Finding Consensus of Circular Strings

환형문자열에 대한 대표문자열을 찾는 병렬 알고리즘

  • 김동희 (인하대학교 컴퓨터정보공학과) ;
  • 심정섭 (인하대학교 컴퓨터정보공학과)
  • Received : 2014.11.20
  • Accepted : 2014.12.29
  • Published : 2015.03.15
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Abstract

The consensus problem is finding a representative string, called a consensus, of a given set S of k strings. Circular strings are different from linear strings in that the last symbol precedes the first symbol. Given a set S of circular strings of length n over an alphabet ${\Sigma}$, we first present an $O({\mid}{\Sigma}{\mid}nlogn)$ time parallel algorithm for finding a consensus of S minimizing both radius and distance sum when k=3 using O(n) threads. Then we present an $O({\mid}{\Sigma}{\mid}n^2logn)$ time parallel algorithm for finding a consensus of S minimizing distance sum when k=4 using O(n) threads. Finally, we compare execution times of our algorithms implemented using CUDA with corresponding sequential algorithms.

대표문자열 문제는 k개의 문자열로 구성된 집합 S가 주어졌을 때 S를 대표하는 한 문자열인 대표문자열을 찾는 문제이다. 환형문자열은 일반적인 문자열과는 달리 문자열의 첫 글자와 마지막 글자가 연결되어 원 모양을 이루는 문자열이다. 본 논문에서는 먼저 k=3이고 길이 n인 환형문자열들로 구성된 S에 대해, 거리반경과 거리합을 동시에 고려한 대표문자열 문제를 O(n)개의 쓰레드를 사용하여 $O({\mid}{\Sigma}{\mid}nlogn)$ 시간에 병렬적으로 해결하는 알고리즘을 제시한다. 이때, ${\Sigma}$는 각 문자열을 구성하는 문자집합이다. 다음으로 k=4이고 길이 n인 환형문자열들로 구성된 S에 대해 거리합 기반 대표문자열 문제를 O(n)개의 쓰레드를 사용하여 $O({\mid}{\Sigma}{\mid}n^2logn)$ 시간에 병렬적으로 해결하는 알고리즘을 제시한다. 이후 두 문제에 대한 병렬 알고리즘들을 CUDA를 이용하여 구현하고 순차 알고리즘들과의 실행 속도를 비교한 결과를 제시한다.

Keywords

Acknowledgement

Supported by : 한국연구재단

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