Improved Time-Space Trade-Offs for Computing Voronoi Diagrams

Banyassady, Bahareh; Korman, Matias; Mulzer, Wolfgang; Renssen, André van; Roeloffzen, Marcel; Seiferth, Paul; Stein, Yannik

doi:10.4230/lipics.stacs.2017.9

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2019

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“…While space-limited algorithms on both RAM and multi-pass models for basic problems have been studied since the early stage of algorithm theory, research in this field has recently intensified. Besides LIS, other frequently studied problems include sorting and selection [27,7,16,30], graph searching [4,14,31,9], geometric computation [10,13,5,1], and k-SUM [39,23].…”

Section: Related Workmentioning

confidence: 99%

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Space-Efficient Algorithms for Longest Increasing Subsequence

et al. 2019

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Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O(n log n) time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For √ n ≤ s ≤ n, we present algorithms that use O(s log n) bits and O( 1 s · n 2 · log n) time for computing the length of a longest increasing subsequence, and O( 1 s · n 2 · log 2 n) time for finding an actual subsequence. We also show that the time complexity of our algorithms is optimal up to polylogarithmic factors in the framework of sequential access algorithms with the prescribed amount of space.

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Section: Related Workmentioning

confidence: 99%

“…For example, consider a sequence τ 1 = 2, 8, 4, 9, 5, 1, 7, 6, 3 . It has an increasing subsequence τ 1 [1,3,5,8] = 2, 4, 5, 6 . Since there is no increasing subsequence of τ 1 with length 5 or more, we have lis(τ 1 ) = 4.…”

Section: Preliminariesmentioning

confidence: 99%