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Truly Sub-cubic Algorithms for Language Edit Distance and RNA Folding via Fast Bounded-Difference Min-Plus Product [article]

Karl Bringmann, Fabrizio Grandoni, Barna Saha, Virginia Vassilevska Williams
2017 arXiv   pre-print
We obtain the first truly sub-cubic algorithm for this bounded-difference (,+)-product (answering an open problem of Chan and Lewenstein).  ...  Valiant for solving context-free grammar parsing with matrix multiplication, yields the first truly sub-cubic algorithms for the following problems: Language Edit Distance (a major problem in the parsing  ...  Acknowledgments The authors would like to thank Uri Zwick for numerous discussions during the initial stages of this project.  ... 
arXiv:1707.05095v1 fatcat:nqclv7nkj5fvfjw3th3cs5gca4

If the Current Clique Algorithms are Optimal, so is Valiant's Parser [article]

Amir Abboud, Arturs Backurs, Virginia Vassilevska Williams
2015 arXiv   pre-print
desirable in practice: RNA Folding, a central problem in computational biology, and Dyck Language Edit Distance, answering an open question of Saha (FOCS'14).  ...  Lee (JACM'01) provided evidence that fast matrix multiplication is needed for CFG parsing, and that very efficient and practical algorithms might be hard or even impossible to obtain.  ...  We would like to thank Piotr Indyk for a discussion that led to this work, and Roy Frostig for introducing us to many modern works on CFG parsing.  ... 
arXiv:1504.01431v2 fatcat:6mvl4a2ewjd55gipq7hhvxvslm

Truly Subcubic Min-Plus Product for Less Structured Matrices, with Applications [article]

Virginia Vassilevska Williams, Yinzhan Xu
2019 arXiv   pre-print
The goal of this paper is to get truly subcubic algorithms for Min-Plus product for less structured inputs than what was previously known, and to apply them to versions of All-Pairs Shortest Paths (APSP  ...  The results are as follows: (1) Our main result is the first truly subcubic algorithm for the Min-Plus product of two n× n matrices A and B with polylog(n) bit integer entries, where B has a partitioning  ...  They also gave several applications of their new algorithm, most no-tably for language edit distance and RNA folding, that were not possible with the prior results on structured Min-Plus product.  ... 
arXiv:1910.04911v1 fatcat:4uoy72cvuvfz7b6g62dqu22bsi

Hardness of RNA Folding Problem with Four Symbols [article]

Yi-Jun Chang
2018 arXiv   pre-print
We also investigate the Dyck edit distance problem, which is a string problem closely related to RNA folding. We demonstrate a reduction from RNA folding to Dyck edit distance with alphabet size 10.  ...  This leads to a much simpler proof of the conditional lower bound for Dyck edit distance problem given by Abboud, Backurs, and Williams (FOCS 2015), and lowers the alphabet size requirement.  ...  The author thanks Seth Pettie for helpful discussions and comments.  ... 
arXiv:1511.04731v3 fatcat:bkv5hsatgnanlitjrihrg5stii

Faster Dynamic Range Mode [article]

Bryce Sandlund, Yinzhan Xu
2020 arXiv   pre-print
The data structure is achieved by combining the ideas in Williams and Xu (SODA 2020) for batch range mode with a novel data structure variant of the Min-Plus product.  ...  In the dynamic range mode problem, we are given a sequence a of length bounded by N and asked to support element insertion, deletion, and queries for the most frequent element of a contiguous subsequence  ...  Acknowledgements We would like to thank Virginia Vassilevska Williams for her valuable comments on a draft of this paper. We would like to thank the anonymous reviewers for their helpful suggestions.  ... 
arXiv:2004.08777v1 fatcat:zqrk444jkvb5fixlmnuf3aukfe

Fine-Grained Complexity of Analyzing Compressed Data: Quantifying Improvements over Decompress-and-Solve

Amir Abboud, Arturs Backurs, Karl Bringmann, Marvin Kunnemann
2017 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)  
.) - Decompress-and-solve is essentially optimal for Context-Free Grammar Parsing and RNA Folding, under the k-Clique conjecture. - We give an algorithm showing that decompress-and-solve is not optimal  ...  Our main results are: - The O(nN√(N/n)) bound for LCS and the O({N N, nM}) bound for Pattern Matching with Wildcards are optimal up to N^o(1) factors, under the Strong Exponential Time Hypothesis.  ...  SETH can explain the lack of O((nN ) 1−ε ) algorithms for problems like LCS on compressed strings.  ... 
doi:10.1109/focs.2017.26 dblp:conf/focs/AbboudBBK17 fatcat:mcpkcysyindwbc3oi5sn5pryvi

Dagstuhl Reports, Volume 6, Issue 11, November 2016, Complete Issue [article]

The talk summarized the development of kernel methods for machine learning, focusing on the main ideas and some future possibilities: introduction of p.d. kernels within the theory of integral equations  ...  distributions by kernel means, underlying kernel tests such as MMD and kernel independence tests.  ...  conditional lower bounds for fundamental string problems such as RNA folding, Dyck edit distance, and k − LCS.  ... 
doi:10.4230/dagrep.6.11 fatcat:tfkdfittpjdydfv7ejvk4bvnh4