Parallel Longest Increasing Subsequence and van Emde Boas Trees
Yan Gu, Ziyang Men, Zheqi Shen, Yihan Sun, Zijin Wan

TL;DR
This paper introduces a simple, efficient parallel algorithm for the longest increasing subsequence problem with optimal work and span, and extends it to a weighted version using parallel van Emde Boas trees, demonstrating superior performance over existing methods.
Contribution
It presents a novel parallel LIS algorithm with optimal work and span, and develops parallel van Emde Boas trees for weighted LIS, improving scalability and efficiency.
Findings
Parallel LIS algorithm costs O(n log k) work and old; span.
Parallel vEB trees support efficient batch operations.
Implementation outperforms existing algorithms on large inputs.
Abstract
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…
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Taxonomy
TopicsAlgorithms and Data Compression · Genomics and Phylogenetic Studies · Advanced Data Storage Technologies
