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Constant factor FPT approximation for capacitated k-median [article]

Marek Adamczyk, Jarosław Byrka, Jan Marcinkowski, Syed M. Meesum, Michał Włodarczyk
2018 arXiv   pre-print
Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem.  ...  In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities.  ...  Subsequently, Li broke this integrality gap barrier by giving a constant factor algorithm for the capacitated k-median by opening (1 + ε) · k facilities [19, 20] .  ... 
arXiv:1809.05791v1 fatcat:fmpu5eczbrhejocmbud5djzsj4

Constant-Factor FPT Approximation for Capacitated k-Median

Marek Adamczyk, Jaroslaw Byrka, Jan Marcinkowski, Syed M. Meesum, Michal Wlodarczyk, Michael Wagner
2019 European Symposium on Algorithms  
Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem.  ...  In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities.  ...  E S A 2 0 1 9 1:8 Constant-Factor FPT Approximation for Capacitated k-Median Definition 8.  ... 
doi:10.4230/lipics.esa.2019.1 dblp:conf/esa/AdamczykBMM019 fatcat:qfnu6mxpfnfbjlsp2nqp3ggyeq

A constant FPT approximation algorithm for hard-capacitated k-means [article]

Yicheng Xu, Rolf H. Möhring, Dachuan Xu, Yong Zhang, Yifei Zou
2019 arXiv   pre-print
As our main contribution, we propose an FPT(k) algorithm with performance guarantee of 69+ϵ for any HCKM instances in this paper.  ...  To the best our knowledge, no constant approximation algorithm or existence proof of such an algorithm is known.  ...  [1] propose a constant FPT approximation for both uniform and nonuniform capacitated k-median, which inspires our work.  ... 
arXiv:1901.04628v3 fatcat:smhtswk2yzcijlxw6jol5yhjsm

On the Fixed-Parameter Tractability of Capacitated Clustering

Vincent Cohen-Addad, Jason Li, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
constant factor exists.  ...  We show that there exists a (3 + )-approximation algorithm for the capacitated k-median and a (9 + )-approximation algorithm for the capacitated k-means problem in general metric spaces whose running times  ...  Indeed, constant factor approximation algorithms are known if the capacities [22, 23] or the number of clusters can be violated by a (1 + ) factor [4, 13] , for constant .  ... 
doi:10.4230/lipics.icalp.2019.41 dblp:conf/icalp/Cohen-AddadL19 fatcat:75222uo6w5h7xbty6rrm4hkjfi

FPT Approximation for Constrained Metric k-Median/Means [article]

Dishant Goyal, Ragesh Jaiswal, Amit Kumar
2020 arXiv   pre-print
We give FPT algorithms with constant approximation guarantee for a range of constrained k-median/means problems.  ...  For this special case, our algorithm gives a (2+ε)-approximation and (4+ε)-approximation for the constrained versions of k-median and k-means problem respectively in FPT time.  ...  Acknowledgements The authors would like to thank Anup Bhattacharya for useful discussions.  ... 
arXiv:2007.11773v1 fatcat:josqnidnabaytcmgdf2wuav2rm

Capacitated Sum-Of-Radii Clustering: An FPT Approximation

Tanmay Inamdar, Kasturi Varadarajan, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
As a warm-up for this result, we also give a constant approximation for the uncapacitated sum of radii clustering problem with matroid constraints, thus obtaining the first FPT approximation for this problem  ...  While constant approximations are known for the uncapacitated version of the problem, there is no work on the capacitated version.  ...  Adapting techniques they develop for capacitated k-median, we can obtain an FPT approximation for capacitated sum of radii in metrics of constant doubling dimension.  ... 
doi:10.4230/lipics.esa.2020.62 dblp:conf/esa/0002V20 fatcat:hhphvg2ucfdvblzoyovctnxvnq

Tight FPT Approximation for Socially Fair Clustering [article]

Dishant Goyal, Ragesh Jaiswal
2021 arXiv   pre-print
We design (3+ε) and (9 + ε) approximation algorithms for the socially fair k-median and k-means problems, respectively, in FPT (fixed parameter tractable) time f(k,ε) · n^O(1), where f(k,ε) = (k/ε)^O(k  ...  Furthermore, we show that if Gap-ETH holds, then better approximation guarantees are not possible in FPT time.  ...  Acknowledgement Thanks to Karthik C.S. for pointing us to the work of Pasin Manurangsi [Man20] .  ... 
arXiv:2106.06755v2 fatcat:2zoqyak7mffaldszq6unlocvjq

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.  ...  Does CAPACITATED k-MEDIAN admit an (1 + 2/e)-approximation algorithm in FPT time with parameter k? Do CAPACITATED EUCLIDEAN k-MEANS/k-MEDIAN admit an EPAS with parameter k or d?  ...  Second, PIH implies that k-CLIQUE is hard to approximate to within any constant factor: Lemma 1. Assuming PIH, there is no constant factor FPT approximation algorithm for k-CLIQUE.  ... 
doi:10.3390/a13060146 fatcat:2u2vv3uksfguvj6473t2gsq42a

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.  ...  Does CAPACITATED k-MEDIAN admit an (1 + 2/e)-approximation algorithm in FPT time with parameter k? Do CAPACITATED EUCLIDEAN k-MEANS/k-MEDIAN admit an EPAS with parameter k or d?  ...  Second, PIH implies that k-CLIQUE is hard to approximate to within any constant factor: Lemma 1. Assuming PIH, there is no constant factor FPT approximation algorithm for k-CLIQUE.  ... 
arXiv:2006.04411v1 fatcat:hjgu7f3s7zbydkcnioq3qlzgza

On the Fixed-Parameter Tractability of Capacitated Clustering [article]

Vincent Cohen-Addad, Jason Li
2022 arXiv   pre-print
constant factor exists.  ...  We show that there exists a (3+ϵ)-approximation algorithm for the capacitated k-median and a (9+ϵ)-approximation algorithm for the capacitated k-means problem in general metric spaces whose running times  ...  Indeed, constant factor approximation algorithms are known if the capacities [22, 23] or the number of clusters can be violated by a (1 + ) factor [4, 13], for constant .  ... 
arXiv:2208.14129v1 fatcat:uvqxy2ky7nazhe7ddq7knxj5iu

A Parameterized Approximation Algorithm for the Chromatic k-Median Problem

Zhen Zhang, Jinchuan Zhang, Lingzhi Zhu
2021 IEEE Access  
In this paper, we give an FPT(k)-time approximation algorithm for chromatic k-median.  ...  The algorithm achieves a (3 + )-approximation and runs in ( We propose a different random sampling algorithm for opening facilities, which is the crucial step in getting the constant factor parameterized  ...  It remains an open problem that whether a constant factor approximation for chromatic k-median can be achieved.  ... 
doi:10.1109/access.2021.3060422 fatcat:yrnbhxxuifca7gq4cmmcj3ejg4

Parameterized Inapproximability for Steiner Orientation by Gap Amplification

Michał Włodarczyk, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
We show that k-Steiner Orientation is unlikely to admit an approximation algorithm with any constant factor, even within FPT running time.  ...  The problem is known to be W[1]-hard when parameterized by k and hard to approximate up to some constant for FPT algorithms assuming Gap-ETH.  ...  For Capacitated k-Median, a constant factor FPT approximation has been obtained [1, 14] , whereas the best-known polynomial-time approximation factor is O(log k).  ... 
doi:10.4230/lipics.icalp.2020.104 dblp:conf/icalp/000120 fatcat:x3myqmzqlnfgdeasbbojyrnqpm

On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications [article]

Sayan Bandyapadhyay, Fedor V. Fomin, Kirill Simonov
2020 arXiv   pre-print
In particular, we obtain the first true constant-approximation algorithm for metric fair clustering, whose running time is fixed-parameter tractable (FPT).  ...  This leads to improved constant-approximations for these problems in general metrics and near-linear time (1+ϵ)-approximations in the Euclidean metric.  ...  The authors are thankful to Vincent Cohen-Addad for sharing the full version of [35] . A Proof of Lemma 4.14 We consider a minimum cost feasible flow φ in G Y for Y = 1.  ... 
arXiv:2007.10137v1 fatcat:4aytetpfg5agvglviignswgisa

Parameterized inapproximability for Steiner Orientation by Gap Amplification [article]

Michał Włodarczyk
2020 arXiv   pre-print
We show that k-Steiner Orientation is unlikely to admit an approximation algorithm with any constant factor, even within FPT running time.  ...  The problem is known to be W[1]-hard when parameterized by k and hard to approximate up to some constant for FPT algorithms assuming Gap-ETH.  ...  For Capacitated k-Median, a constant factor FPT approximation has been obtained [1] , whereas the best-known polynomial-time approximation factor is O(log k).  ... 
arXiv:1907.06529v3 fatcat:awyzxap73na2zkbmo2rcinup4q

Lossy Kernelization of Same-Size Clustering [article]

Sayan Bandyapadhyay, Fedor V. Fomin, Petr A. Golovach, Nidhi Purohit, Kirill Simonov
2021 arXiv   pre-print
In this work, we study the k-median clustering problem with an additional equal-size constraint on the clusters, from the perspective of parameterized preprocessing.  ...  Our main result is the first lossy (2-approximate) polynomial kernel for this problem, parameterized by the cost of clustering.  ...  It includes tight algorithmic and complexity results for k-means and k-median [13] and constant factor FPT-approximation for capacitated clustering [14] .  ... 
arXiv:2107.07383v1 fatcat:unbmeiysaza6rcxpesfxz7g5lu
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