2012/07/02 by Kevin Leckey, Leckey, Kevin, Ralph Neininger +3
Computer Science · Mathematics · #60F05 #68P05 #68Q25 #Algorithms and Data Compression #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Natural Language Processing Techniques #Network Packet Processing and Optimization #Probability (math.PR) #cs.DS #math.PR #msc:60F05 #msc:68P05 #msc:68Q25
paper · pdf · doi:10.48550/arxiv.1207.0302
minor revision; to appear in Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA) (2013)
openalex publication_date 2012/07/02 · arxiv created 2012/09/18 · arxiv updated 2012/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP addresses lookup, from data compression (i.e., Lempel-Ziv'77 scheme) to dynamic hashing, from partial-match queries to speech recognition, from leader election algorithms to distributed hashing tables and graph compression. While the performance of tries under a realistic probabilistic model is of significant importance, its analysis, even for simplest memoryless sources, has proved difficult. Rigorous findings about inherently complex parameters were rarely analyzed (with a few notable exceptions) under more realistic models of string generations. In this paper we meet these challenges: By a novel use of the contraction method combined with analytic techniques we prove a central limit theorem for the external path length of a trie under a general Markov source. In particular, our results apply to the Lempel-Ziv'77 code. We envision that the methods described here will have further applications to other trie parameters and data structures.