A dynamic programming algorithm for input estimation on linear time-variant systems

We study the problem of folding a polyomino [Formula: see text] into a polycube [Formula: see text], allowing faces of [Formula: see text] to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of [Formula: see text] or can divide squares in half (diagonally and/or orthogonally), (b) must be mountain or can be both mountain and valley, (c) can remain flat (forming an angle of [Formula: see text]), and (d) must lie on just the polycube surface or can have interior faces as well. Second, we give all the inclusion relations among all models that fold on the grid lines of [Formula: see text]. Third, we characterize all polyominoes that can fold into a unit cube, in some models. Fourth, we give a linear-time dynamic programming algorithm to fold a tree-shaped polyomino into a constant-size polycube, in some models. Finally, we consider the triangular version of the problem, characterizing which polyiamonds fold into a regular tetrahedron.

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Ubiquitous Wireless Power Transfer for Multiple Mobile Devices

10.5753/ctd.2021.15764 ◽

2021 ◽

Author(s):

Alexander Decker de Souza ◽

Luiz Filipe Menezes Vieira ◽

Marcos Augusto Menezes Vieira

Keyword(s):

Dynamic Programming ◽

Mobile Devices ◽

Linear Time ◽

Greedy Algorithms ◽

Dynamic Programming Algorithm ◽

Wireless Power Transfer ◽

Programming Algorithm ◽

Power Transfer ◽

Wireless Power ◽

Programming Algorithms

We propose two new computational problems associated with the charging of mobile devices using wireless power transfer via magnetic induction. Algorithms for these problems may enable ubiquitous charging, meaning the user is no longer required to be aware of the devices charging processes. We prove both problems as being NP-Hard and propose three dynamic programming algorithms to solve them in linear time regarding the size of the time horizon. We also propose three greedy algorithms for the problems. Experiments indicate that the best dynamic-programming algorithm among those proposed reaches between 89% and 97% of effectiveness, while the best greedy reaches between 74% and 92%, depending on the considered scenario.

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LinearFold: linear-time approximate RNA folding by 5'-to-3' dynamic programming and beam search

Bioinformatics ◽

10.1093/bioinformatics/btz375 ◽

2019 ◽

Vol 35 (14) ◽

pp. i295-i304 ◽

Cited By ~ 10

Author(s):

Liang Huang ◽

He Zhang ◽

Dezhong Deng ◽

Kai Zhao ◽

Kaibo Liu ◽

...

Keyword(s):

Dynamic Programming ◽

Computational Linguistics ◽

Rna Folding ◽

Linear Time ◽

Dynamic Programming Algorithm ◽

Optimal Solution ◽

Supplementary Information ◽

Programming Algorithm ◽

Time Dynamic ◽

Approximate Search

Abstract Motivation Predicting the secondary structure of an ribonucleic acid (RNA) sequence is useful in many applications. Existing algorithms [based on dynamic programming] suffer from a major limitation: their runtimes scale cubically with the RNA length, and this slowness limits their use in genome-wide applications. Results We present a novel alternative O(n3)-time dynamic programming algorithm for RNA folding that is amenable to heuristics that make it run in O(n) time and O(n) space, while producing a high-quality approximation to the optimal solution. Inspired by incremental parsing for context-free grammars in computational linguistics, our alternative dynamic programming algorithm scans the sequence in a left-to-right (5′-to-3′) direction rather than in a bottom-up fashion, which allows us to employ the effective beam pruning heuristic. Our work, though inexact, is the first RNA folding algorithm to achieve linear runtime (and linear space) without imposing constraints on the output structure. Surprisingly, our approximate search results in even higher overall accuracy on a diverse database of sequences with known structures. More interestingly, it leads to significantly more accurate predictions on the longest sequence families in that database (16S and 23S Ribosomal RNAs), as well as improved accuracies for long-range base pairs (500+ nucleotides apart), both of which are well known to be challenging for the current models. Availability and implementation Our source code is available at https://github.com/LinearFold/LinearFold, and our webserver is at http://linearfold.org (sequence limit: 100 000nt). Supplementary information Supplementary data are available at Bioinformatics online.

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