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A Technique for Obtaining True Approximations for k-Center with Covering Constraints [article]

Georg Anegg, Haris Angelidakis, Adam Kurpisz, Rico Zenklusen
2020 arXiv   pre-print
In this paper, we introduce a new approach to deal with such covering constraints that leads to (true) approximations, including a 4-approximation for Colorful k-Center with constantly many colors—settling  ...  an open question raised by Bandyapadhyay, Inamdar, Pai, and Varadarajan—and a 4-approximation for Fair Robust k-Center, for which the existence of a (true) constant-factor approximation was also open.  ...  Conclusion In this work, we presented a technique for obtaining true constant-factor approximation algorithms for k-center problems with multiple covering constraints on the points to be covered.  ... 
arXiv:2007.03946v1 fatcat:sn44ukw63vhnvfisdvskz7drte

A technique for obtaining true approximations for k-center with covering constraints

Georg Anegg, Haris Angelidakis, Adam Kurpisz, Rico Zenklusen
2021 Mathematical programming  
In this paper, we introduce a new approach to deal with such covering constraints that leads to (true) approximations, including a 4-approximation for Colorful k-Center with constantly many colors—settling  ...  an open question raised by Bandyapadhyay, Inamdar, Pai, and Varadarajan—and a 4-approximation for Fair Robust k-Center, for which the existence of a (true) constant-factor approximation was also open.  ...  However, the resulting slight reduction in running time from O(γ q 2 M γ ) to O(q 2 M γ ) is irrelevant for our purposes.  ... 
doi:10.1007/s10107-021-01645-y pmid:35300156 pmcid:PMC8907128 fatcat:w6xnmsfqhjbu3e7nf57o25ccu4

Linearization of Euclidean norm dependent inequalities applied to multibeam satellites design

Jean-Thomas Camino, Christian Artigues, Laurent Houssin, Stéphane Mourgues
2019 Computational optimization and applications  
We first empirically compare this linearization approach with a previously proposed linearization approach of the literature on the continuous kcenter problem.  ...  problem at the cost of entirely controllable approximations even for non convex constraints.  ...  Below we apply this technique to the kcenter problem so as to make an experimental comparison with our approach for different discretization levels.  ... 
doi:10.1007/s10589-019-00083-z fatcat:wqgsipfkzfhijocd3meadqzq24

Maximum Target Coverage Problem in Mobile Wireless Sensor Networks

Dieyan Liang, Hong Shen, Lin Chen
2020 Sensors  
Given a set of targets to be covered and a set of mobile sensors, we seek a sensor dispatch algorithm maximizing the covered targets under the constraint that the maximal moving distance for each sensor  ...  We also design a deterministic approximation algorithm with nearly ▵−1 approximation ratio by using a colouring technique, where ▵ denotes the maximal number of subsets covering the same target.  ...  Taking quantization error into consideration, the approximation ratio is calculate the number of targets covered by each colour k; 10: end for 11: obtain colour q with the maximum number of covered  ... 
doi:10.3390/s21010184 pmid:33383935 fatcat:7sa4ceopkfburny37amdsq2weq

Privacy Preserving Clustering with Constraints

Clemens Rösner, Melanie Schmidt, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We raise the question whether general methods can be derived to turn an approximation algorithm for a clustering problem with some constraints into an approximation algorithm that respects one constraint  ...  The k-center problem is a classical combinatorial optimization problem which asks to find k centers such that the maximum distance of any input point in a set P to its assigned center is minimized.  ...  for k-center to obtain a 9-approximation [15, 5].  ... 
doi:10.4230/lipics.icalp.2018.96 dblp:conf/icalp/Rosner018 fatcat:45ap4hrdefg33nrovc6mcemnzi

On Some Variants of Euclidean K-Supplier [article]

Euiwoong Lee, and Viswanath Nagarajan, Lily Wang
2021 arXiv   pre-print
We obtain (1+√(3))-approximation algorithms for both variants, which are the first improvements over the previously-known factor-3 approximation (that is known to be best-possible for general metrics).  ...  We study two variants of k-Supplier, namely Priority k-Supplier and k-Supplier with Outliers, in Euclidean metrics.  ...  [CLLW13] obtained a 3-approximation algorithm for this problem as well. Results and Techniques.  ... 
arXiv:2112.01700v1 fatcat:fpawemnfn5dqljpoqi34g36e4i

Anchor-Based Localization via Interval Analysis for Mobile Ad-Hoc Sensor Networks

F. Mourad, H. Snoussi, F. Abdallah, C. Richard
2009 IEEE Transactions on Signal Processing  
Location awareness is a fundamental requirement for many applications of sensor networks. This paper proposes an original technique for self-localization in mobile ad-hoc networks.  ...  The problem is then formulated as a constraint satisfaction problem where a simple Waltz algorithm is applied in order to contract the solution.  ...  The novelty of our work is that we define locations as intervals covering all acceptable solutions with respect to the given constraints instead of using approximated values.  ... 
doi:10.1109/tsp.2009.2020018 fatcat:rwv5do5ssvbqfja2eoums7nuxm

Deployment Strategies of Multiple Aerial BSs for User Coverage and Power Efficiency Maximization

Jingcong Sun, Christos Masouros
2019 IEEE Transactions on Communications  
Finally, we propose a robust technique for compensating the loss of coverage probability in the existence of inaccurate user location information.  ...  Then, we investigate a deployment method based on K-means clustering.  ...  Thus, the coverage area of the k-th aerial BS can be approximated as a circle region centered at (x ck , y ck ), with radius R k = h k tan θB 2 , and the user i is associated with the k-th aerial BS, when  ... 
doi:10.1109/tcomm.2018.2889460 fatcat:74ybl2kslzfazkswl4byvmpcpi

Coresets for constrained k-median and k-means clustering in low dimensional Euclidean space [article]

Melanie Schmidt, Julian Wargalla
2021 arXiv   pre-print
We demonstrate that a technique proposed in 2019 for solving a specific constrained streaming k-means problem, namely fair k-means clustering, actually implies streaming algorithms for all these constraints  ...  We study (Euclidean) k-median and k-means with constraints in the streaming model.  ...  We thank anonymous referees for their helpful feedback and pointing out typos.  ... 
arXiv:2106.07319v1 fatcat:6q4hbna7mbbkjcdgyekpiv4v3m

Symbolic Execution Enhanced System Testing [chapter]

Misty Davies, Corina S. Păsăreanu, Vishwanath Raman
2012 Lecture Notes in Computer Science  
We use machine learning techniques -treatment learning and function fitting-to approximate the system input constraints that will lead to the satisfaction of the unit constraints.  ...  The symbolic execution computes unit constraints at run-time, along program paths obtained by system simulations.  ...  For a constraints tree T and a path σ = n 1 , n 2 , . . . , n k of nodes in T , such that n 1 , n 2 , . . . , n k are covered with witness sets V 1 , V 2 , . . . , V k at the system level and corresponding  ... 
doi:10.1007/978-3-642-27705-4_23 fatcat:qkjmu3wuynfcrpnk3c336l2cwq

Privacy preserving clustering with constraints [article]

Clemens Rösner, Melanie Schmidt
2018 arXiv   pre-print
We raise the question whether general methods can be derived to turn an approximation algorithm for a clustering problem with some constraints into an approximation algorithm that respects one constraint  ...  The k-center problem is a classical combinatorial optimization problem which asks to find k centers such that the maximum distance of any input point in a set P to its assigned center is minimized.  ...  for k-center to obtain a 9-approximation [14, 4] .  ... 
arXiv:1802.02497v2 fatcat:cwgzfqq5ozbkbdiaooob5deplq

Approximation Algorithms for Minimum-Load k-Facility Location

Sara Ahmadian, Babak Behsaz, Zachary Friggstad, Amin Jorati, Mohammad R. Salavatipour, Chaitanya Swamy
2018 ACM Transactions on Algorithms  
Our main result is the first polynomial time approximation scheme (PTAS) for MLkFL on line metrics (note that no non-trivial true approximation of any kind was known for this metric).  ...  This problem was studied under the name of min-max star cover in [6, 2] , who (among other results) gave bicriteria approximation algorithms for MLkFL for when F = C.  ...  Obviously, the major open question here is to obtain a true approximation (even an O(log n)-approximation) for the MLkFL on general metrics.  ... 
doi:10.1145/3173047 fatcat:hqlywbuhlbflbhvn3krbao675u

Separated Red Blue Center Clustering [article]

Marzieh Eskandari and Bhavika B. Khare and Nirman Kumar
2021 arXiv   pre-print
We provide an approximation algorithm for this problem, and a polynomial time algorithm for the constrained problem, where all the centers must lie on a line ℓ.  ...  We study a generalization of k-center clustering, first introduced by Kavand et. al., where instead of one set of centers, we have two types of centers, p red and q blue, and where each red center is at  ...  Here we show an approximation algorithm for the problem as well as one with a better approximation factor for the constrained problem.  ... 
arXiv:2107.07914v1 fatcat:viabeaj2ezgy7m7faqwkkwox7q

Faster Deterministic Approximation Algorithms for Correlation Clustering and Cluster Deletion [article]

Nate Veldt
2021 arXiv   pre-print
Our results include 4-approximation algorithms for cluster deletion and correlation clustering, based on simplified linear programs with far fewer constraints than the canonical relaxations.  ...  Although many approximation algorithms have been designed for this problem, the best theoretical results rely on obtaining lower bounds via expensive linear programming relaxations.  ...  In particular, we can easily obtain a 2-approximation for minSTC by finding a maximal matching in the Gallai graph of G = (V, E) and using it to get a 2-approximation for vertex cover in the Gallai graph  ... 
arXiv:2111.10699v1 fatcat:xbbgjhs5rbfurcyaq6f6t6uacu

Minimizing Uncertainty through Sensor Placement with Angle Constraints [article]

Ioana O. Bercea, Volkan Isler, Samir Khuller
2016 arXiv   pre-print
, a feature that generic Set Cover techniques do not account for.  ...  When the angular coverage is required to be at least (1-1/δ)·α, we obtain a O(δ)- approximation for sensor placement with α-coverage on the plane.  ...  In general, techniques for k-center provide approximation guarantees by first showing a lower bound on the optimal solution size.  ... 
arXiv:1607.05791v1 fatcat:wg4g7qpylfcujlk2ieles3m424
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