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Target Counting under Minimal Sensing: Complexity and Approximations [chapter]

Sorabh Gandhi, Rajesh Kumar, Subhash Suri
2008 Lecture Notes in Computer Science  
We consider the problem of counting a set of discrete point targets using a network of sensors under a minimalistic model.  ...  , to be followed by more expensive sensing and localization if needed.  ...  In this paper, we examine some of these key issues in the context of counting and localizing targets in a physical space under minimal sensing assumptions.  ... 
doi:10.1007/978-3-540-92862-1_4 fatcat:iwuinwta6remphe7m22okqx3jq

Belief Tracking for Planning with Sensing: Width, Complexity and Approximations

B. Bonet, H. Geffner
2014 The Journal of Artificial Intelligence Research  
Second, we introduce a meaningful, powerful, and sound approximation scheme, beam tracking, that is exponential in a smaller parameter, the problem causal width, and has much broader applicability.  ...  bounded and small.  ...  Hector Geffner is partially supported by EU FP7 Grant# 270019 (Spacebook) and MICINN CSD2010-00034 (Simulpast).  ... 
doi:10.1613/jair.4475 fatcat:ddvdzws3mzbh5ddpejyfvxc2na

SYSTEM IDENTIFICATION, APPROXIMATION AND COMPLEXITY

BRIAN R. GAINES
1977 International Journal of General Systems  
An admissible model is such that any less complex model is a worse approximation.  ...  It is proved under very general assumptions that, if deterministic models are required then nearly all behaviours require models of nearly maximum complexity.  ...  I am grateful to Michael Arbib, Richard Dawkins, Joe Goguen, George Klir, Ladislav Kohout, Steve Matheson and Roger Moore, for helpful discussions and comments, and to Judea Pearl of UCLA for detailed  ... 
doi:10.1080/03081077708934759 fatcat:tcot4dyj6rccnhgtoo73rktv4i

Approximate resilience, monotonicity, and the complexity of agnostic learning [article]

Dana Dachman-Soled and Vitaly Feldman and Li-Yang Tan and Andrew Wan and Karl Wimmer
2014 arXiv   pre-print
This characterization is based on the duality between ℓ_1 approximation by degree-d polynomials and approximate d-resilience that we establish.  ...  We show that approximate resilience essentially characterizes the complexity of agnostic learning of a concept class C over the uniform distribution.  ...  We thank Udi Wieder and Yuval Peres for helpful information about the CycleRun function, and Ryan O'Donnell, Johan Håstad, Rocco Servedio and Jan Vondrák for helpful conversations.  ... 
arXiv:1405.5268v2 fatcat:vwqvnuquqbdxddfcog5amr6ocm

Optimal harmonic period assignment: complexity results and approximation algorithms

Morteza Mohaqeqi, Mitra Nasri, Yang Xu, Anton Cervin, Karl-Erik Årzén
2018 Real-time systems  
Corollary 1 The approximation error with Algorithm 1 is smaller than 2, i.e., J J * < 2.  ...  Also, if there is no release jitter and execution time variation, RM and EDF generate the same schedule for each instance of a task.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s11241-018-9304-0 fatcat:oo75csoggjhplnzsdggrtrfu5y

Approximation and Parameterized Complexity of Minimax Approval Voting [article]

Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat
2016 arXiv   pre-print
for Closest String due to Ma and Sun [SIAM J.  ...  We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes.  ...  [24] is essentially optimal, and indeed, in this sense Minimax Approval Voting is harder than Closest String.  ... 
arXiv:1607.07906v1 fatcat:zq63yrsslnewlc4cuvfwspmemm

Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity [article]

Markus Bachmayr, Wolfgang Dahmen
2019 arXiv   pre-print
In particular, we highlight the role of adaptivity when dealing with such strongly nonlinear methods that integrate in a natural way issues of discrete and continuous accuracy.  ...  This is the guiding question throughout this article, which reviews recent developments of low-rank approximation methods for problems in high spatial dimensions.  ...  For v ∈ H and η > 0, let r(v, η) := min{r : (∃ w ∈ S r : v − w ≤ η)}, which is the minimal complexity parameter for which the best approximation from these sets attains accuracy η.  ... 
arXiv:1910.07052v1 fatcat:57rcy3cgh5b7dh4writcqnjrkm

The aperiodic complexities and connections to dimensions and Diophantine approximation [article]

Viktor Schroeder, Steffen Weil
2015 arXiv   pre-print
We compare them to well-know complexities such as the box-dimension and the topological entropy.  ...  Using this condition we introduce two new quantities F, G, called the 'aperiodic complexities', of the system and establish relations between F, G with the topology and geometry of X.  ...  Both authors acknowledge the support by the Swiss National Science Foundation (grant no. 135091) and the referee for the detailed comments and corrections.  ... 
arXiv:1506.00955v1 fatcat:nmgivqilwzhvlfajro5btdl2iu

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

Andrei A. Bulatov, Venkatesan Guruswami, Andrei Krokhin, Dániel Marx, Marc Herbstritt
2016 Dagstuhl Reports  
The Dagstuhl Seminar 15301 "The Constraint Satisfaction Problem: Complexity and Approximability" was aimed at bringing together researchers using all the different techniques in the study of the CSP, so  ...  combinatorics, have been used to analyze both the computational complexity and approximabilty of algorithmic tasks related to the constraint satisfaction problem (CSP), as well as the applicability/limitations  ...  Joint work with Yoichi Iwata and Magnus Wahlström. For each algebra A, we count the minimal number g(n) of generators of A n as a function of n.  ... 
doi:10.4230/dagrep.5.7.22 dblp:journals/dagstuhl-reports/BulatovGKM15 fatcat:lcyvfsxsbzbrfe27irlpxepxoi

The computational complexity and approximability of a series of geometric covering problems

M. Yu. Khachai, M. I. Poberii
2013 Proceedings of the Steklov Institute of Mathematics  
We consider a series of geometric problems of covering finite subsets of finitedimensional numerical spaces by minimal families of hyperplanes. We prove that the problems are hard and Max-SNP-hard.  ...  (project nos. 12-P-1-1016 and 12-S-1-1017/1).  ...  ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research (project nos. 10-01-00273 and 10-07-00134) and by the Presidium of the Ural Branch of the Russian Academy of Sciences  ... 
doi:10.1134/s008154381309006x fatcat:y752al3fynautiisnsf7q3ej2i

Approximate resilience, monotonicity, and the complexity of agnostic learning [chapter]

Dana Dachman-Soled, Vitaly Feldman, Li-Yang Tan, Andrew Wan, Karl Wimmer
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
This characterization is based on the duality between ℓ 1 approximation by degree-d polynomials and approximate d-resilience that we establish.  ...  We show that approximate resilience essentially characterizes the complexity of agnostic learning of a concept class C over the uniform distribution.  ...  Acknowledgements We thank Udi Wieder and Yuval Peres for helpful information about the CycleRun function.  ... 
doi:10.1137/1.9781611973730.34 dblp:conf/soda/Dachman-SoledFTWW15 fatcat:hsqwgnhnwzaexnqoiihqsxh22m

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms [article]

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 arXiv   pre-print
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  It indicates that a characterization of approximabilities for the minimization versions will be more complex and challenging.  ... 
arXiv:2006.04411v1 fatcat:hjgu7f3s7zbydkcnioq3qlzgza

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 Algorithms  
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  under standard complexity assumptions.  ... 
doi:10.3390/a13060146 fatcat:2u2vv3uksfguvj6473t2gsq42a

Stable Marriage and Roommates problems with restricted edges: Complexity and approximability

Ágnes Cseh, David F. Manlove
2016 Discrete Optimization  
For non-bipartite Stable Roommates instances, case (2) yields an NP-hard but (under some cardinality assumptions) 2-approximable problem.  ...  We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden.  ...  Acknowledgements We would like to thank the anonymous reviewers of this paper and an earlier version of it for their valuable comments, which helped to improve the presentation, and for suggesting several  ... 
doi:10.1016/j.disopt.2016.03.002 fatcat:x2fr2o7yynd7xhq22pgzjzl2ni

Stable Marriage and Roommates Problems with Restricted Edges: Complexity and Approximability [chapter]

Ágnes Cseh, David F. Manlove
2015 Lecture Notes in Computer Science  
For non-bipartite Stable Roommates instances, case (2) yields an NP-hard but (under some cardinality assumptions) 2-approximable problem.  ...  We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden.  ...  Acknowledgements We would like to thank the anonymous reviewers of this paper and an earlier version of it for their valuable comments, which helped to improve the presentation, and for suggesting several  ... 
doi:10.1007/978-3-662-48433-3_2 fatcat:z2sgva74evblhg2r4hned3huvy
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