A Probabilistic Model Revealing Shortcomings in Lua's Hybrid Tables
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Lua (Ierusalimschy et al., 1996) is a well-known scripting language, popular among many programmers, most notably in the gaming industry. Remarkably, the only data-structuring mechanism in Lua, is an associative array called a table. With Lua 5.0, the reference implementation of Lua introduced hybrid tables to implement tables using both a hash table and a dynamically growing array combined together: the values associated with integer keys are stored in the array part, when suitable. All this is transparent to the user, which has a unique simple interface to handle tables. In this paper we carry out a theoretical analysis of the performance of Lua's tables, by considering various worst-case and probabilistic scenarios. In particular, we uncover some problematic situations for the simple probabilistic model where we add a new key with some fixed probability p>1/2 and delete a key with probability 1-p: the cost of performing T such operations is proved to be Ω(Tlog T) with high probability, instead of linear in T.
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