An Approximation Framework for Bounded Facility Location Problems

We study the bounded metric uncapacitated facility location (bUFL) problem and its two variants, the bounded fault-tolerant facility location (bFTFL) problem and the bounded fault-tolerant facility placement (bFTFP) problem. We propose a unified approximation framework built on the state-of-the-art approximation algorithms for the three unbounded counterparts, leading to a \((2.488 + \epsilon )\)-approximation algorithm for the bUFL problem in the Euclidean plane, a \((1.488+H(n))\)-approximation algorithm for the bUFL problem, a \((1.725+H(n))\)-approximation algorithm for the bFTFL problem, and a \((1.515+H(n))\)-approximation algorithm for the bFTFP problem in a general metric space. We also prove an inapproximability result for all the three bounded facility location problems in a general metric space.

[1]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[2]  Roberto Solis-Oba,et al.  Approximation Algorithms for Bounded Facility Location Problems , 2001, J. Comb. Optim..

[3]  Chaitanya Swamy,et al.  Fault-tolerant facility location , 2003, SODA '03.

[4]  Sudipto Guha,et al.  Improved combinatorial algorithms for the facility location and k-median problems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[5]  Milan Ruzic,et al.  Uniform deterministic dictionaries , 2008, TALG.

[6]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[7]  Aravind Srinivasan,et al.  Fault-Tolerant Facility Location: A Randomized Dependent LP-Rounding Algorithm , 2010, IPCO.

[8]  Samir Khuller,et al.  Algorithms for facility location problems with outliers , 2001, SODA '01.

[9]  Vijay V. Vazirani,et al.  Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs , 1999, SIAM J. Comput..

[10]  David Steurer,et al.  Analytical approach to parallel repetition , 2013, STOC.

[11]  Sudipto Guha,et al.  A constant factor approximation algorithm for the fault-tolerant facility location problem , 2003, J. Algorithms.

[12]  Weng Kerui.  Approximation algorithm for uniform bounded facility location problem , 2013 .

[13]  Vijay V. Vazirani,et al.  An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem , 2003, Algorithmica.

[14]  Shi Li.  A 1.488 approximation algorithm for the uncapacitated facility location problem , 2013, Inf. Comput..

[15]  Hong Shen,et al.  The Fault-Tolerant Facility Allocation Problem , 2009, ISAAC.

[16]  Amin Saberi,et al.  A new greedy approach for facility location problems , 2002, STOC '02.

[17]  Jaroslaw Byrka,et al.  Improved Approximation Algorithm for Fault-Tolerant Facility Placement , 2014, WAOA.

[18]  Rajmohan Rajaraman,et al.  Analysis of a local search heuristic for facility location problems , 2000, SODA '98.

[19]  Fabián A. Chudak,et al.  Improved Approximation Algorithms for the Uncapacitated Facility Location Problem , 2003, SIAM J. Comput..

[20]  Marek Chrobak,et al.  LP-rounding algorithms for the fault-tolerant facility placement problem , 2015, J. Discrete Algorithms.

[21]  Dorit S. Hochbaum,et al.  Heuristics for the fixed cost median problem , 1982, Math. Program..

[22]  Jian Li,et al.  A PTAS for the Weighted Unit Disk Cover Problem , 2015, ICALP.

[23]  Changyuan Yu,et al.  A 5+epsilon-approximation algorithm for minimum weighted dominating set in unit disk graph , 2009, Theor. Comput. Sci..

[24]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[25]  Marek Chrobak,et al.  Approximation algorithms for the Fault-Tolerant Facility Placement problem , 2011, Inf. Process. Lett..

[26]  Jaroslaw Byrka.  An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem , 2007, APPROX-RANDOM.

[27]  Éva Tardos,et al.  Approximation algorithms for facility location problems (extended abstract) , 1997, STOC '97.

[28]  Mohammad Mahdian,et al.  Approximation Algorithms for Metric Facility Location Problems , 2006, SIAM J. Comput..

[29]  Evangelos Markakis,et al.  Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP , 2002, JACM.

[30]  Jinhui Xu,et al.  An improved approximation algorithm for uncapacitated facility location problem with penalties , 2005, J. Comb. Optim..