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| Approximation Algorithm for the Metric Uncapacitated Facility Location Problems |
| Jing RUAN |
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Abstract In this paper, two approximation algorithms based on linear programming
rounding techniques for the uncapacitated facility location problems are
provided. The performance guarantee of the approximation algorithms reduces
from 4 to 3. The reason is that the random choice of facility allows us to
include the assignment cost $C_j^\ast $ in the analysis, instead of bounding
only the facility cost by $OPT_{ILP} $, but bound both the facility cost and
part of the assignment cost by $OPT_{ILP} $. Both of two linear programming
rounding techniques solve the relaxation of the integer program for
uncapacitated facility location and rounding the solution.
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