Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Analyzing Problem Instance Space Based on Difficulty-distance Correlation

난이도-거리 상관관계 기반의 문제 인스턴스 공간 분석

  • 전소영 (한국과학기술원 전산학과) ;
  • 김용혁 (광운대학교 컴퓨터소프트웨어학과)
  • Received : 2011.12.28
  • Accepted : 2012.07.26
  • Published : 2012.08.25
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Abstract

Finding or automatically generating problem instance is useful for algorithm analysis/test. The topic has been of interest in the field of hardware/software engineering and theory of computation. We apply objective value-distance correlation analysis to problem spaces, as previous researchers applied it to solution spaces. According to problems, we define the objective function by (1) execution time of tested algorithm or (2) its optimality; this definition is interpreted as difficulty of the problem instance being solved. Our correlation analysis is based on the following aspects: (1) change of correlation when we use different algorithms or different distance functions for the same problem, (2) change of that when we improve the tested algorithm, (3) relation between a problem instance space and the solution space for the same problem. Our research demonstrates the way of problem instance space analysis and will accelerate the problem instance space analysis as an initiative research.

문제 인스턴스 탐색 혹은 자동 생성은 알고리즘 분석 및 테스트에 적용될 수 있으며, 하드웨어, 소프트웨어 프로그램, 계산 이론 등 다양한 수준에서 연구되어온 주제이다. 본 연구에서는 해(解) 공간에 사용된 목적값-거리 상관관계 분석을 문제 인스턴스 공간에 적용하였다. 문제 인스턴스의 목적값은 문제에 따라 알고리즘의 수행 시간과 최적해를 잘 구하는 정도로 정의하였다. 이러한 정의는 문제 인스턴스의 난이도로 해석할 수 있다. 상관관계는 3가지 측면에서 분석하였다: 첫째, 알고리즘과 거리 함수에 따른 상관관계 차이, 둘째, 알고리즘의 개선 전/후의 상관관계 변화, 셋째, 문제 인스턴스 공간과 해당 문제의 해 공간 사이의 연관성. 본 논문은 문제 인스턴스 공간에 상관계수 분석이 어떻게 적용될 수 있는지 보여주며, 문제 인스턴스 공간 분석을 본격적으로 다루는 첫번째 시도이다.

Keywords

References

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