Theoretical and Practical Improvements on the RMQ-Problem, with Applications to LCA and LCE
- Cite this paper as:
- Fischer J., Heun V. (2006) Theoretical and Practical Improvements on the RMQ-Problem, with Applications to LCA and LCE. In: Lewenstein M., Valiente G. (eds) Combinatorial Pattern Matching. CPM 2006. Lecture Notes in Computer Science, vol 4009. Springer, Berlin, Heidelberg
The Range-Minimum-Query-Problem is to preprocess an array such that the position of the minimum element between two specified indices can be obtained efficiently. We present a direct algorithm for the general RMQ-problem with linear preprocessing time and constant query time, without making use of any dynamic data structure. It consumes less than half of the space that is needed by the method by Berkman and Vishkin. We use our new algorithm for RMQ to improve on LCA-computation for binary trees, and further give a constant-time LCE-algorithm solely based on arrays. Both LCA and LCE have important applications, e.g., in computational biology. Experimental studies show that our new method is almost twice as fast in practice as previous approaches, and asymptotically slower variants of the constant-time algorithms perform even better for today’s common problem sizes.
Unable to display preview. Download preview PDF.