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The aim of this paper is to give a comprehensive comparison of well-known longest common subsequence algorithms (for two input strings) and study their behaviour in various application environments. The performance of the methods depends heavily on the properties of the problem instance as well as the supporting data structures used in the implementation. We want to make also a clear distinction between methods that determine the actual lcs and those calculating only its length, since the execution time and more importantly, the space demand depends crucially on the type of the task. To our knowledge, this is the first time this kind of survey has been done. Due to the page limits, the paper gives only a coarse overview of the performance of the algorithms; more detailed studies are reported elsewhere.