Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
SIAM Journal on Computing
Suffix arrays: a new method for on-line string searches
SIAM Journal on Computing
The complexity of searching a sorted array of strings
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A tight lower bound for searching a sorted array
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
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
The Complexity of Some Simple Retrieval Problems
Journal of the ACM (JACM)
Tight Bounds for Searching a Sorted Array of Strings
SIAM Journal on Computing
On a multidimensional search problem (Preliminary Version)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A quick tour on suffix arrays and compressed suffix arrays
Theoretical Computer Science
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Questions about order versus disorder in systems and models have been fascinating scientists over the years. In computer science, order is intimately related to sorting, commonly meant as the task of arranging keys in increasing or decreasing order with respect to an underlying total order relation. The sorted organization is amenable for searching a set of n keys, since each search requires Θ(log n) comparisons in the worst case, which is optimal if the cost of a single comparison can be considered a constant. Nevertheless, we prove that disorder implicitly provides more information than order does. For the general case of searching an array of multidimensional keys whose comparison cost is proportional to their length (and hence which cannot be considered a constant), we demonstrate that “suitable” disorder gives better bounds than those derivable by using the natural lexicographic order. We start from previous work done by Andersson et al. [2001], who proved that Θ(k log log n/log log(4 + klog log n/log n) + k + log n) character comparisons (or probes) comprise the tight complexity for searching a plain sorted array of n keys, each of length k, arranged in lexicographic order. We describe a novel permutation of the n keys that is different from the sorted order. When keys are kept “unsorted” in the array according to this permutation, the complexity of searching drops to Θ(k + log n) character comparisons (or probes) in the worst case, which is optimal among all possible permutations, up to a constant factor. Consequently, disorder carries more information than does order; this fact was not observable before, since the latter two bounds are Θ(log n) when k = O(1). More implications are discussed in the article, including searching in the bit-probe model.