Simple Linear Comparison of Strings in V-order*

Alatabbi, Ali; Daykin, Jacqueline W.; Rahman, M. Sohel; Smyth, W. Franklin

doi:10.3233/fi-2015-1228

Cited by 5 publications

(8 citation statements)

References 23 publications

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“…Now, the efficiency of ADRS algorithm depends on a key result (cf. Corollary 2.9 of [2]) which proves that the mismatch position of the two strings under comparison remains the same as we go deep into the recursion. This fact along with the result presented in Lemma 5 gives us yet another idea for an efficient string comparison algorithm in V -order.…”

Section: -Order String Comparisonmentioning

confidence: 54%

“…Recently, Alatabbi et al presented an interesting V -order string comparison algorithm in [1,2] (referred to as the ADRS algorithm henceforth), where a mapping of the position of each letter in the string is exploited to check for the conditions stated in Lemma 1. Note that there are three conditions in Lemma 1 and things get most interesting when we reach Condition (C3) because of its recursive nature.…”

Section: -Order String Comparisonmentioning

confidence: 99%

“…Step 4: Merge the sorted suffixes in Step 2 using ADRS algorithm [2] to obtain the suffix array of v 1 v 2 . For the merge, if v j ≻ v k , then the chosen suffix for the new array is v k , otherwise it is v j v k .…”

Section: Suffix Sorting and Burrows Wheeler Transformationmentioning

confidence: 99%

“…In particular, we relate V -order string comparison to lexicographic by showing how it is possible to traverse the strings from left to right, respectively right to left, at each stage determining in O(1) time the order of prefixes, respectively suffixes. This improves on existing ordering algorithms [1,2,7] in various ways: it removes any dependence on an "indexed" alphabet, it orders prefixes and suffixes in addition to the original strings, and it reduces dependence on additional data structures. Furthermore, we introduce an input-sensitive variant for V -order comparison.…”

Section: Introductionmentioning

confidence: 96%

See 3 more Smart Citations

String Comparison in $V$-Order: New Lexicographic Properties & On-line Applications

Alatabbi¹,

Daykin²,

Rahman³

et al. 2015

Preprint

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V -order is a global order on strings related to Unique Maximal Factorization Families (UMFFs) [6,7], which are themselves generalizations of Lyndon words [14]. V -order has recently been proposed as an alternative to lexicographical order in the computation of suffix arrays and in the suffix-sorting induced by the Burrows-Wheeler transform.Efficient V -ordering of strings thus becomes a matter of considerable interest. In this paper we present new and surprising results on V -order in strings, then go on to explore the algorithmic consequences.

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Section: -Order String Comparisonmentioning

confidence: 54%

Section: -Order String Comparisonmentioning

confidence: 99%

Section: Suffix Sorting and Burrows Wheeler Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

String Comparison in $V$-Order: New Lexicographic Properties & On-line Applications

Alatabbi¹,

Daykin²,

Rahman³

et al. 2015

Preprint

Self Cite

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“…We show that this order is the same as the lexicographical order over Lyndon words but are different over primitive words and finite words. It is also different from reflected lexicographic order, colexicographic order, shortlex order, Kleene-Brouwer order, V-Order, alternative order [11,9,3,2,1]. It seems that order ≤ ∞ has not been reported in literature.…”

Section: Introductionmentioning

confidence: 99%

String Rearrangement Inequalities and a Total Order Between Primitive Words

Luo¹,

Taikun²,

Jia³

2022

Preprint

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We study the following rearrangement problem: Given n words, rearrange and concatenate them so that the obtained string is lexicographically smallest (or largest, respectively). We show that this problem reduces to sorting the given words so that their repeating strings are non-decreasing (or non-increasing, respectively), where the repeating string of a word A refers to the infinite string AAA . . .. Moreover, for fixed size alphabet Σ, we design an O(L) time sorting algorithm of the words (in the mentioned orders), where L denotes the total length of the input words. Hence we obtain an O(L) time algorithm for the rearrangement problem. Finally, we point out that comparing primitive words via comparing their repeating strings leads to a total order, which can further be extended to a total order on the finite words (or all words).

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