Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
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SIAM Journal on Computing
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International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Solution of a linear recurrence equation arising in the analysis of some algorithms
SIAM Journal on Algebraic and Discrete Methods
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The evaluation of an alternative sum with applications to the analysis of some data structures
Information Processing Letters
Some results on V-ary asymmetric tries
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The art of computer programming, volume 3: (2nd ed.) sorting and searching
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ACM Transactions on Database Systems (TODS)
Handbook of Algorithms
Data Structures and Algorithms
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Laws of large numbers and tail inequalities for random tries and PATRICIA trees
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Limit laws for the height in PATRICIA tries
Journal of Algorithms - Analysis of algorithms
Summary Structures for Frequency Queries on Large Transaction Sets
DCC '00 Proceedings of the Conference on Data Compression
Improved Behaviour of Tries by the "Symmetrization" of the Source
DCC '02 Proceedings of the Data Compression Conference
On zone-balancing of peer-to-peer networks: analysis of random node join
Proceedings of the joint international conference on Measurement and modeling of computer systems
Clustering and indexing of experience sequences for popularity-driven recommendations
Proceedings of the 3rd ACM workshop on Continuous archival and retrival of personal experences
Average case analysis of algorithms
Algorithms and theory of computation handbook
Removing uncertainties from overlay network
DASFAA'11 Proceedings of the 16th international conference on Database systems for advanced applications - Volume Part I
Renewal theory in the analysis of tries and strings
Theoretical Computer Science
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HiPEAC'05 Proceedings of the First international conference on High Performance Embedded Architectures and Compilers
A framework for scalable distributed provenance storage system
Computer Standards & Interfaces
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The Patricia trie is a simple modification of a regular trie. By eliminating unary branching nodes, the Patricia achieves better performance than regular tries. However, the question is: how much on the average is the Patricia better? This paper offers a thorough answer to this question by considering some statistics of the number of nodes examined in a successful search and an unsuccessful search in the Patricia tries. It is shown that for the Patricia containing n records the average of the successful search length Sn asymptotically becomes 1/h1 · ln n + O(1), and the variance of Sn is either var Sn = c · ln n + 0(1) for an asymmetric Patricia or var Sn = 0(1) for a symmetric Patricia, where h1 is the entropy of the alphabet over which the Patricia is built and c is an explicit constant. Higher moments of Sn are also assessed. The number of nodes examined in an unsuccessful search Un is studied only for binary symmetric Patricia tries. We prove that the mth moment of the unsuccessful search length EUmn satisfies limn→∞ EUmn/logm2n = 1, and the variance of Un is var Un = 0.87907. These results suggest that Patricia tries are very well balanced trees in the sense that a random shape of Patriciatries resembles the shape of complete trees that are ultimately balanced trees.