Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Mellin transforms and asymptotics: harmonic sums
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Fast algorithms for sorting and searching strings
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
The number of bit comparisons used by Quicksort: an average-case analysis
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The Number of Symbol Comparisons in QuickSort and QuickSelect
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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We consider the complexity of sorting strings in the model that counts comparisons between symbols and not just comparisons between strings. We show that for any set of strings S the complexity of sorting S can naturally be expressed in terms of the trie induced by S. This holds not only for lower bounds but also for the running times of various algorithms. Thus this "data-specific" analysis allows a direct comparison of different algorithms running on the same data. We give such "data-specific" analyses for various versions of quicksort and versions of mergesort. As a corollary we arrive at a very simple analysis of quicksorting random strings, which so far required rather sophisticated mathematical tools. As part of this we provide insights in the analysis of tries of random strings which may be interesting in their own right.