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Unifying and Strengthening Hardness for Dynamic Problems via the Online Matrix-Vector Multiplication Conjecture

Monika Henzinger, Sebastian Krinninger, Danupon Nanongkai, Thatchaphol Saranurak
2015 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15  
Consider the following Online Boolean Matrix-Vector Multiplication problem: We are given an n× n matrix M and will receive n column-vectors of size n, denoted by v_1,...,v_n, one by one.  ...  The conjecture also leads to hardness results for problems that were previously based on diverse problems and conjectures, such as 3SUM, combinatorial Boolean matrix multiplication, triangle detection,  ...  Saranurak would like to thank Markus Bläser and Gorav Jindal for discussions.  ... 
doi:10.1145/2746539.2746609 dblp:conf/stoc/HenzingerKNS15 fatcat:f2koopjznrgcfoiflcbmf7r4rq

Conditional Hardness for Sensitivity Problems

Monika Henzinger, Andrea Lincoln, Stefan Neumann, Virginia Vassilevska Williams, Marc Herbstritt
2017 Innovations in Theoretical Computer Science  
For example, we show that under the Boolean Matrix Multiplication (BMM) conjecture combinatorial algorithms cannot compute the (4/3 − ε)-approximate diameter of an undirected unweighted dense graph with  ...  This is intriguing, as in the static setting it is a big open problem whether Diameter is as hard as APSP.  ...  Unifying and strengthening hardness for dynamic problems via the online matrix-vector multiplication conjecture. In STOC, pages 21-30, 2015. 28 Monika Henzinger and Stefan Neumann.  ... 
doi:10.4230/lipics.itcs.2017.26 dblp:conf/innovations/HenzingerL0W17 fatcat:6mw52rwkafcothehbz4nua27wq

One Algorithm to Evaluate Them All: Unified Linear Algebra Based Approach to Evaluate Both Regular and Context-Free Path Queries [article]

Ekaterina Shemetova, Rustam Azimov, Egor Orachev, Ilya Epelbaum, Semyon Grigorev
2021 arXiv   pre-print
Thus, we provide the alternative way to construct a slightly subcubic algorithm for CFPQ which is based on linear algebra and incremental transitive closure (a classic graph-theoretic problem), as opposed  ...  Our evaluation shows that our algorithm is a good candidate to be the universal algorithm for both regular and context-free path querying.  ...  Acknowledgements We are grateful to Ekaterina Verbitskaia for careful reading and pointing out some mistakes.  ... 
arXiv:2103.14688v1 fatcat:fy73vloj5zcmjbbwis37rbexte

How Fast Can We Play Tetris Greedily With Rectangular Pieces? [article]

Justin Dallant, John Iacono
2022 arXiv   pre-print
We show via a reduction to the Multiphase problem [Pătraşcu, 2010] that on a board of width w=Θ(n), if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time  ...  The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture.  ...  Acknowledgements We thank Nemau for involuntarily providing us with the initial inspiration for this work.  ... 
arXiv:2202.10771v2 fatcat:npv4akt6izbnvecyfqf35qkmyy

Distributed Online Optimization in Dynamic Environments Using Mirror Descent [article]

Shahin Shahrampour, Ali Jadbabaie
2016 arXiv   pre-print
We demonstrate the application of our method to decentralized tracking of dynamic parameters and verify the results via numerical experiments.  ...  We establish a regret bound that scales inversely in the spectral gap of the network, and more notably it represents the deviation of minimizer sequence with respect to the given dynamics.  ...  However, as studied in the centralized online optimization [19] - [22] , the hardness of the problem can be characterized via a complexly measure that captures the variation in the minimizer sequence  ... 
arXiv:1609.02845v1 fatcat:iyifrjdkqfbobbhn7itkaf2xyu

Conditional Hardness for Sensitivity Problems [article]

Monika Henzinger, Andrea Lincoln, Stefan Neumann, Virginia Vassilevska Williams
2017 arXiv   pre-print
For example, we show that under the Boolean Matrix Multiplication (BMM) conjecture combinatorial algorithms cannot compute the (4/3 - ϵ)-approximate diameter of an undirected unweighted dense graph with  ...  We give more lower bounds under the Strong Exponential Time Hypothesis and the All Pairs Shortest Paths Conjecture.  ...  Unifying and strengthening hardness for dynamic problems via the online matrix-vector multiplication conjecture. In STOC, pages 21-30, 2015. 28 Monika Henzinger and Stefan Neumann.  ... 
arXiv:1703.01638v1 fatcat:udwtdffcebbijku3zkctq4x4ii

Dynamic Parameterized Network for CTR Prediction [article]

Jian Zhu, Congcong Liu, Pei Wang, Xiwei Zhao, Guangpeng Chen, Junsheng Jin, Changping Peng, Zhangang Lin, Jingping Shao
2021 arXiv   pre-print
Our Dynamic Parameterized Networks significantly outperforms state-of-the-art methods in the offline experiments on the public dataset and real-world production dataset, together with an online A/B test  ...  extra DNN modules for implicit interaction modeling.  ...  High-order message can be processed with non-linear function layer by layer, which is hard to be found useful via multiplicative models.  ... 
arXiv:2111.04983v1 fatcat:2pg76hstz5asjfxy4qou2epqu4

Person Re-identification: A Retrospective on Domain Specific Open Challenges and Future Trends [article]

Asmat Zahra, Nazia Perwaiz, Muhammad Shahzad, Muhammad Moazam Fraz
2022 arXiv   pre-print
., occlusion, pose scale \& viewpoint variance, background clutter, person misalignment and cross-domain generalization across camera modalities, which makes the problem of re-Id still far from being solved  ...  Majority of the proposed approaches directly or indirectly aim to solve one or multiple of these existing challenges.  ...  of the input vector by a matrix, then by another matrix, and then the computation of resultant vector.  ... 
arXiv:2202.13121v1 fatcat:luwwbcwspndqpauj4dosmmojee

Cross-Domain Recommender Systems [chapter]

Iván Cantador, Ignacio Fernández-Tobías, Shlomo Berkovsky, Paolo Cremonesi
2015 Recommender Systems Handbook  
and sparsity problems in a target domain, or enabling personalized crossselling recommendations for items from multiple domains.  ...  The proliferation of e-commerce sites and online social media has allowed users to provide preference feedback and maintain profiles in multiple systems, reflecting a variety of their tastes and interests  ...  preference dynamics can be captured.  ... 
doi:10.1007/978-1-4899-7637-6_27 fatcat:4kregbpxajbnxmg6xywfmm22ki

CHAOS: Accurate and Realtime Detection of Aging-Oriented Failure Using Entropy [article]

Pengfei Chen, Yong Qi, Di Hou
2015 arXiv   pre-print
Via theoretical proof and experimental evaluation, we demonstrate that MMSE satisfies Stability, Monotonicity and Integration which we conjecture that an ideal aging indicator should have.  ...  These chronic problems often fly under the radar of software monitoring systems before causing severe impacts (e.g. system failure).  ...  ACKNOWLEDGMENTS The authors would like to thank all the members in our research group and the anonymous reviewers.  ... 
arXiv:1502.00781v1 fatcat:hc7uqeoi35fmbd2ogszxwsn52m

Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

Henrique F. da Cruz, Rosário Fernandes, Susana Furtado
2017 Linear Algebra and its Applications  
Twenty-seven years later we are gathered here for the second such conference organised in the Island of Malta.  ...  We have received 150 abstracts for 20-minute contributed talks which will run in four parallel sessions and cover a large variety of areas within graph theory and combinatorics.  ...  The boundary-type sets are rather trivial for trees and are all subsets of the leaves. We provide a characterization of ∂(G), Ct(G), and Ext(G) for the family of MOPs.  ... 
doi:10.1016/j.laa.2017.05.014 fatcat:zlcp5rb2sjeqvlyaajvf2nyoby

Introduction to Online Convex Optimization [article]

Elad Hazan
2021 arXiv   pre-print
It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed.  ...  In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization.  ...  I am very thankful to Wouter Koolen-Wijkstra for a helpful suggestion in the analysis of the Online Newton Step algorithm.  ... 
arXiv:1909.05207v2 fatcat:2fvtye3uo5dajjy4hfdwk33lbq

A Probabilistic Reinforcement-Based Approach To Conceptualization

Hadi Firouzi, Majid Nili Ahmadabadi, Babak N. Araabi
2008 Zenodo  
Moreover the probabilistic formation of the concepts is employed to deal with uncertain and dynamic nature of real problems in addition to the ability of generalization.  ...  Experimental results, on the other hand, show the applicability and effectiveness of the proposed method in continuous and noisy environments for a real robotic task such as maze as well as the benefits  ...  Based on issues discussed till now, the original problem can be reduced to the problem of online reinforcement-based classification and clustering of the perceptual space in order to get the similarity  ... 
doi:10.5281/zenodo.1078317 fatcat:cofo6zvtv5f7ldh3gwz4vyem2y

Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching [article]

Arun Jambulapati, Yujia Jin, Aaron Sidford, Kevin Tian
2022 arXiv   pre-print
These results improve upon the previous best runtime of Õ(m ·ϵ^-4) [BGS20] and illustrate the utility of using regularized optimization problem solvers for designing dynamic algorithms.  ...  We give a generic framework which reduces this dynamic matching problem to solving regularized graph-structured optimization problems to high accuracy.  ...  Acknowledgements We thank anonymous reviewers for their feedback, Amin Saberi and David Wajc for helpful conversations, Jason Altschuler for providing a reference for the unaccelerated convergence rate  ... 
arXiv:2204.12721v3 fatcat:qe65bhaeordnjhrsl77v5fywoi

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  A v ariation of bundle methods is presented by means of which such a t ype of problems can be solved.In this variation a dynamic polyhedral model of dom is generated by means of normal vectors.In addition  ...  Each iteration of the algorithm performs a small number of matrix-vector and vector-vector multiplications that take full advantage of the sparsity of the original data plus a small number of other operations  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa
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