## Lower Bound Techniques for Data Structures (2008)

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### BibTeX

@MISC{Patrascu08lowerbound,

author = {Mihai Patrascu},

title = {Lower Bound Techniques for Data Structures},

year = {2008}

}

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### Abstract

We describe new techniques for proving lower bounds on data-structure problems, with the following broad consequences: â¢ the first Î©(lgn) lower bound for any dynamic problem, improving on a bound that had been standing since 1989; â¢ for static data structures, the first separation between linear and polynomial space. Specifically, for some problems that have constant query time when polynomial space is allowed, we can show Î©(lg n/ lg lg n) bounds when the space is O(n Â· polylog n). Using these techniques, we analyze a variety of central data-structure problems, and obtain improved lower bounds for the following: â¢ the partial-sums problem (a fundamental application of augmented binary search trees); â¢ the predecessor problem (which is equivalent to IP lookup in Internet routers); â¢ dynamic trees and dynamic connectivity; â¢ orthogonal range stabbing; â¢ orthogonal range counting, and orthogonal range reporting; â¢ the partial match problem (searching with wild-cards); â¢ (1 + Îµ)-approximate near neighbor on the hypercube; â¢ approximate nearest neighbor in the lâ metric. Our new techniques lead to surprisingly non-technical proofs. For several problems, we obtain simpler proofs for bounds that were already known.