4,605 research outputs found
Centrality of Trees for Capacitated k-Center
There is a large discrepancy in our understanding of uncapacitated and
capacitated versions of network location problems. This is perhaps best
illustrated by the classical k-center problem: there is a simple tight
2-approximation algorithm for the uncapacitated version whereas the first
constant factor approximation algorithm for the general version with capacities
was only recently obtained by using an intricate rounding algorithm that
achieves an approximation guarantee in the hundreds.
Our paper aims to bridge this discrepancy. For the capacitated k-center
problem, we give a simple algorithm with a clean analysis that allows us to
prove an approximation guarantee of 9. It uses the standard LP relaxation and
comes close to settling the integrality gap (after necessary preprocessing),
which is narrowed down to either 7, 8 or 9. The algorithm proceeds by first
reducing to special tree instances, and then solves such instances optimally.
Our concept of tree instances is quite versatile, and applies to natural
variants of the capacitated k-center problem for which we also obtain improved
algorithms. Finally, we give evidence to show that more powerful preprocessing
could lead to better algorithms, by giving an approximation algorithm that
beats the integrality gap for instances where all non-zero capacities are
uniform.Comment: 21 pages, 2 figure
Constant-Factor FPT Approximation for Capacitated k-Median
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 a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicative factor were obtained. However, to produce solutions without violations appears to be hard and potentially requires different algorithmic techniques. Notably, if parameterized by the number of facilities k, the problem is also W[2] hard, making the existence of an exact FPT algorithm unlikely. In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities. The algorithm runs in time 2^O(k log k) n^O(1) and achieves an approximation ratio of 7+epsilon
A simple dual ascent algorithm for the multilevel facility location problem
We present a simple dual ascent method for the multilevel facility location problem which finds a solution within times the optimum for the uncapacitated case and within times the optimum for the capacitated one. The algorithm is deterministic and based on the primal-dual technique. \u
An Improved Approximation Algorithm for the Hard Uniform Capacitated k-median Problem
In the -median problem, given a set of locations, the goal is to select a
subset of at most centers so as to minimize the total cost of connecting
each location to its nearest center. We study the uniform hard capacitated
version of the -median problem, in which each selected center can only serve
a limited number of locations.
Inspired by the algorithm of Charikar, Guha, Tardos and Shmoys, we give a
-approximation algorithm for this problem with increasing the
capacities by a factor of , which improves
the previous best -approximation algorithm proposed by Byrka,
Fleszar, Rybicki and Spoerhase violating the capacities by factor
.Comment: 19 pages, 1 figur
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