3,741 research outputs found
Space-Efficient Algorithms for Longest Increasing Subsequence
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 sqrt(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
Parallel Longest Increasing Subsequence and van Emde Boas Trees
This paper studies parallel algorithms for the longest increasing subsequence
(LIS) problem. Let be the input size and be the LIS length of the
input. Sequentially, LIS is a simple problem that can be solved using dynamic
programming (DP) in work. However, parallelizing LIS is a
long-standing challenge. We are unaware of any parallel LIS algorithm that has
optimal work and non-trivial parallelism (i.e., or
span).
This paper proposes a parallel LIS algorithm that costs work,
span, and space, and is much simpler than the previous
parallel LIS algorithms. We also generalize the algorithm to a weighted version
of LIS, which maximizes the weighted sum for all objects in an increasing
subsequence. To achieve a better work bound for the weighted LIS algorithm, we
designed parallel algorithms for the van Emde Boas (vEB) tree, which has the
same structure as the sequential vEB tree, and supports work-efficient parallel
batch insertion, deletion, and range queries.
We also implemented our parallel LIS algorithms. Our implementation is
light-weighted, efficient, and scalable. On input size , our LIS
algorithm outperforms a highly-optimized sequential algorithm (with cost) on inputs with . Our algorithm is also much faster
than the best existing parallel implementation by Shen et al. (2022) on all
input instances.Comment: to be published in Proceedings of the 35th ACM Symposium on
Parallelism in Algorithms and Architectures (SPAA '23
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