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New Sublinear Algorithms and Lower Bounds for LIS Estimation [article]

Ilan Newman, Nithin Varma
2021 arXiv   pre-print
In this paper, we give the first nontrivial lower bound on the complexity of LIS estimation, and also provide novel algorithms that complement our lower bound.  ...  There are no better lower bounds for LIS estimation than the obvious bounds implied by testing monotonicity (for adaptive or nonadaptive algorithms).  ...  Lower Bounds for Nonadaptive LIS Estimation In this section, we prove our lower bounds (Theorem 1.1) on the query complexity of 2-sided error nonadaptive algorithms for estimating the distance of real-valued  ... 
arXiv:2010.05805v3 fatcat:sv6ebhuacnarlfs75g2k3wocka

New Sublinear Algorithms and Lower Bounds for LIS Estimation

Ilan Newman, Nithin Varma, Nikhil Bansal, Emanuela Merelli, James Worrell
2021
There are no better lower bounds for LIS estimation than the obvious bounds implied by testing monotonicity (for adaptive or nonadaptive algorithms).  ...  In this paper, we give the first nontrivial lower bound on the complexity of LIS estimation, and also provide novel algorithms that complement our lower bound.  ...  I C A L P 2 0 2 1 100:16 New Sublinear Algorithms and Lower Bounds for LIS Estimation A β-dense box may have density that is anything in [β, 1] .  ... 
doi:10.4230/lipics.icalp.2021.100 fatcat:cllf2by75zfaznhl65wbvmvvqu

Edit Distance to Monotonicity in Sliding Windows [chapter]

Ho-Leung Chan, Tak-Wah Lam, Lap-Kei Lee, Jiangwei Pan, Hing-Fung Ting, Qin Zhang
2011 Lecture Notes in Computer Science  
Motivated by applications on network quality monitoring, we extend the study to estimating the edit distance to monotonicity of a sliding window covering the w most recent items in the stream for any w  ...  We give a deterministic algorithm which can return an estimate within a factor of (4 + ) using O( 1 2 log 2 ( w)) space. We also extend the study in two directions.  ...  We thank the anonymous reviewers for helpful comments and for pointing out the randomized lower bounds to us.  ... 
doi:10.1007/978-3-642-25591-5_58 fatcat:5p3u52ztwjgl3mydyzpdtmomvi

Edit Distance to Monotonicity in Sliding Windows [article]

Ho-Leung Chan, Tak-Wah Lam, Lap-Kei Lee, Jiangwei Pan, Hing-Fung Ting, Qin Zhang
2011 arXiv   pre-print
Motivated by applications on network quality monitoring, we extend the study to estimating the edit distance to monotonicity of a sliding window covering the w most recent items in the stream for any w  ...  We give a deterministic algorithm which can return an estimate within a factor of (4+) using O(1/^2^2( w)) space. We also extend the study in two directions.  ...  Acknowledgement We thank the anonymous reviewers for helpful comments and for pointing out the randomized lower bounds to us.  ... 
arXiv:1111.5386v1 fatcat:yeryqismwrgk5i7nddufusowoy

Fast Bounds on the Distribution of Smooth Numbers [chapter]

Scott T. Parsell, Jonathan P. Sorenson
2006 Lecture Notes in Computer Science  
In this paper we present improvements to Bernstein's algorithm, which finds rigorous upper and lower bounds for Ψ (x, y). Bernstein's original algorithm runs in time roughly linear in y.  ...  In particular, if log y is a fractional power of log x, which is true in applications to factoring and cryptography, then our new algorithm has a running time that is polynomial in log y, and gives bounds  ...  Define n ± i , our upper and lower bound estimates for n i , as follows: -For i ≤ α lg z, n − i := n + i := n i .  ... 
doi:10.1007/11792086_13 fatcat:vkyo4r5zanhrla2p63g5cvzjga

Some large-scale matrix computation problems

Zhaojun Bai, Gark Fahey, Gene Golub
1996 Journal of Computational and Applied Mathematics  
We will study a practical numerical algorithm for bounding the bilinear form, where the matrix A is only referenced through matrix-vector multiplications.  ...  All these computational tasks are related to the central mathematical problem studied in this paper, namely, bounding the bilinear form uXf(A)v for a given matrix A and vectors u and v, wherefis a given  ...  Acknowledgements The authors would like to thank Keh-Fei Liu and Shao-Jian Dong for bringing to our attention the applications of problem (1) in the lattice QCD, and thank Shao-Jian Dong for providing  ... 
doi:10.1016/0377-0427(96)00018-0 fatcat:uqqx6f6icbc2xhsfnqji3ezcdq

Long-term production planning problem: scheduling, makespan estimation and bottleneck analysis

Dmitry I. Arkhipov, Olga Battaïa, Alexander A. Lazarev
2017 IFAC-PapersOnLine  
The makespan estimation algorithm is tested on the well-known PSPLIB benchmark library where the best known lower bounds are improved for 5 instances.  ...  The makespan estimation algorithm is tested on the well-known PSPLIB benchmark library where the best known lower bounds are improved for 5 instances.  ...  Makespan lower bound estimation The obtained result lead us to a new makespan lower bound estimation Algorithm M EA. It can be formulated as follows. 1.  ... 
doi:10.1016/j.ifacol.2017.08.991 fatcat:td62uptnz5hvxiagqieqxeugae

Single-Machine Scheduling with Fixed Periodic Preventive Maintenance to Minimise the Total Weighted Completion Times

Hongming Zhou, Ya-Chih Tsai, Shenquan Huang, Yarong Chen, Fuh-Der Chou, Bekir Sahin
2021 Mathematical Problems in Engineering  
To evaluate the performances of the proposed heuristic algorithms, two new lower bounds are further developed.  ...  This problem is proven to be NP-hard; a position-based mixed integer programming model and an efficient heuristic algorithm with local improvement strategy are developed for the total weighted completion  ...  For the 1, h k |nr| w i C i problem, we proposed a new MIP model, two new lower bounds, and a heuristic algorithm. e proposed heuristic algorithm adopted a bin-packing scheme that considers batch formation  ... 
doi:10.1155/2021/8891322 fatcat:dasuyop3brhvnl3voxqim2ibjq

EECBS: A Bounded-Suboptimal Search for Multi-Agent Path Finding [article]

Jiaoyang Li, Wheeler Ruml, Sven Koenig
2021 arXiv   pre-print
Motivated by Explicit Estimation Search (EES), we propose Explicit Estimation CBS (EECBS), a new bounded-suboptimal variant of CBS, that uses online learning to obtain inadmissible estimates of the cost  ...  We hope that the scalability of EECBS enables additional applications for bounded-suboptimal MAPF algorithms.  ...  We then present our new algorithm EECBS, which uses Explicit Estimation Search (EES) at the high level and uses online learning to estimate solution cost.  ... 
arXiv:2010.01367v2 fatcat:4bcpffcrkzacrnhfv27ovmxqee

Numerical Methods of Complex Valued Linear Algebraic System

Shi-Liang Wu, Shu-Qian Shen, Masoud Hajarian, Jia Liu, Lev A. Krukier
2015 Journal of Applied Mathematics  
And some new inequalities on the lower bound for the minimal eigenvalue of the corresponding matrix and the corresponding eigenvector are presented to establish an upper bound for the ℓ 1 -norm of the  ...  Shen present two new types of Newton method for computing the nonsingular square root of a matrix and provide convergence theorems and stability analysis for these new proposed algorithms. L.  ...  Acknowledgments The guest editors of this special issue would express their sincere gratitude to all the authors and anonymous reviewers who have generously contributed to this special issue.  ... 
doi:10.1155/2015/979234 fatcat:gys22hqi7fbsrivy66tqpter3i

Open Problem: Best Arm Identification: Almost Instance-Wise Optimality and the Gap Entropy Conjecture [article]

Lijie Chen, Jian Li
2016 arXiv   pre-print
Moreover, we introduce a new quantity, called the gap entropy for a best-arm problem instance, and conjecture that it is the instance-wise lower bound.  ...  However, we conjecture that modulo the additive term Ω(Δ_2^-2Δ_2^-1) (which is an upper bound and worst case lower bound for the 2-arm problem), there is an instance optimal algorithm for BEST-1-ARM.  ...  We believe the difficulty can be overcome by additional new algorithmic ideas. Lower Bounds: In Chen and Li (2015) , we prove the following lower bound, improving the MT lower bound.  ... 
arXiv:1605.08481v1 fatcat:yjypzlmeebfaxc7bnmwr2d7h4a

Precisely Verifying the Null Space Conditions in Compressed Sensing: A Sandwiching Algorithm [article]

Myung Cho, Weiyu Xu
2013 arXiv   pre-print
In this paper, we first propose a series of new polynomial-time algorithms to compute upper bounds on α_k.  ...  Empirical results show the performance improvements of our algorithm over existing known methods; and our algorithm outputs precise values of α_k, with much lower complexity than exhaustive search.  ...  Algorithm for computing exact value of α k in description * Global Upper Bound (GUB): the current upper bound α k * Global Lower Bound (GLB): the current lower bound for α k * Cheap Upper Bound (CUB):  ... 
arXiv:1306.2665v3 fatcat:2ru5wkxm7vdwpbjliditrr52iq

Network link tomography and compressive sensing

Rhys Alistair Bowden, Matthew Roughan, Nigel Bean
2011 Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems - SIGMETRICS '11  
to find the new bounds.  ...  In the final step, each link i that has a lower bound li the same as its upper bound ui we consider solved, and eliminate it from the remaining measurement equations.  ... 
doi:10.1145/1993744.1993805 dblp:conf/sigmetrics/BowdenRB11 fatcat:5scclmgqevetdf5ifycsxzojti

Network link tomography and compressive sensing

Rhys Alistair Bowden, Matthew Roughan, Nigel Bean
2011 Performance Evaluation Review  
to find the new bounds.  ...  In the final step, each link i that has a lower bound li the same as its upper bound ui we consider solved, and eliminate it from the remaining measurement equations.  ... 
doi:10.1145/2007116.2007172 fatcat:frhmdkvtufdilgsvqhumaa6x4i

Page 3783 of Mathematical Reviews Vol. , Issue 88g [page]

1988 Mathematical Reviews  
A. (2-YAR) Nonpolynomial lower bounds for the complexity of optimization problems of clique and vertex covering in a class of direct algorithms.  ...  (H-EOTVO) Tight worst-case bounds for bin packing algorithms. Theory of algorithms (Pécs, 1984), 233-240, Collog. Math. Soc. Janos Bolyai, 44, North-Holland, Amsterdam-New York, 1985.  ... 
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