Improving Order with Queues
Andreas Karrenbauer, Kurt Mehlhorn, Pranabendu Misra, Paolo Luigi Rinaldi, Anna Twelsiek, Alireza Haqi, Siavash Rahimi Shateranloo

TL;DR
This paper explores how to improve sequence sorting using multiple FIFO queues, providing optimal algorithms for LDS reduction, merging sequences, and reducing down-steps, with applications in manufacturing.
Contribution
It introduces an optimal patience sort-based algorithm for LDS reduction with k queues, characterizes mergeability of sequences based on LDS, and offers an online algorithm for reducing down-steps.
Findings
The LDS can be reduced by up to k-1 using k queues.
Merging two sequences with LDS 2 is not always possible, but always possible with LDS 3.
An optimal online algorithm reduces down-steps in sequences.
Abstract
Given a sequence of numbers and parallel First-in-First-Out (FIFO) queues, how close can one bring the sequence to sorted order? It is known that queues suffice to sort the sequence if the Longest Decreasing Subsequence (LDS) of the input sequence is at most . But, what if the number of queues is too small for sorting completely? - We give a simple algorithm, based on Patience Sort, that reduces the LDS by . We also show, that the algorithm is optimal, i.e., for any there exists a sequence of LDS such that the LDS cannot be reduced below with queues. - Merging two sorted queues is at the core of Merge Sort. In contrast, two sequences of LDS two cannot always be merged into a sequence of LDS two. We characterize when it is possible and give an algorithm to decide whether it is possible. Merging into a sequence of LDS three is always…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgorithms and Data Compression · Optimization and Packing Problems · Optimization and Search Problems
