Simplified stable merging tasks

Salowe, Jeffrey S.; Steiger, William L.

doi:10.1016/0196-6774(87)90050-2

Cited by 39 publications

(48 citation statements)

References 8 publications

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“…This seems surprising, given the close relation between planar convex hulls and sorting, and the large body of literature on space-efficient sorting and merging algorithms [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The main reason for this is probably that the scan portion of Graham's original algorithm [1] is inherently in-place, so in-place sorting algorithms already provide an O(n log n) time in-place convex hull algorithm.…”

Section: Introductionmentioning

confidence: 99%

Space-efficient planar convex hull algorithms*1

Brönnimann¹

2004

Theoretical Computer Science

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Section: Introductionmentioning

confidence: 99%

Space-efficient planar convex hull algorithms*1

Brönnimann¹

2004

Theoretical Computer Science

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“…Lemma 2 (Salowe and Steiger [9]). Given arrays A and B of total length n, we can merge A and B in-place using a comparison-based algorithm in O(n) time.…”

Section: Lemma 1 (Franceschini Et Al [8])mentioning

confidence: 99%

Space-Efficient Re-Pair Compression

Bille

Gørtz

Prezza

2017

2017 Data Compression Conference (DCC)

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Re-Pair [1] is an effective grammar-based compression scheme achieving strong compression rates in practice. Let n, σ, and d be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original paper, the authors show how to compute the Re-Pair grammar in expected linear time and 5n + 4σ 2 + 4d + √ n words of working space on top of the text. In this work, we propose two algorithms improving on the space of their original solution. Our model assumes a memory word of log 2 n bits and a re-writable input text composed by n such words. Our first algorithm runs in expected O(n/ ) time and uses (1 + )n + √ n words of space on top of the text for any parameter 0 < ≤ 1 chosen in advance. Our second algorithm runs in expected O(n log n) time and improves the space to n + √ n words.

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“…We employ the in-place mergesort of [21] and pay a slowdown of O(k) in the time complexity, since we run it on O(n/ log n) vectors, each of length k. The cost is O(k × (n/ log n) log(n/ log n)) = O(nk) time.…”

Section: High-level Descriptionmentioning

confidence: 99%

“…We use a few optimal algorithmic tools for atomic keys: in-place stable mergesort and in-place merge [21]; in-place selection for order statistics [17]. We apply these algorithms to vectors in a straightforward way by paying a slowdown of O(k) per elementary step in their time complexity.…”

Section: High-level Descriptionmentioning

confidence: 99%