# Improved Local Search Algorithm for Universal Facility Location

In a recent result, M. P\'{a}l \etal \cite{pal01facility} showed that a local search heuristic can be used to obtain a $9 + \epsilon$ approximation for capacitated facility location with {\em hard capacities}, also known as 1-CFL. Later, P\'{a}l, and Mahdian~\cite{MP03} showed that more powerful local operations can be used to obtain $8+\epsilon$ approximation for the Universal Facility Location Problem which includes 1-CFL as a special case. After scaling, their algorithm achieves an approximation ratio of $7.88 + \epsilon$.

We improve these results incrementally on two fronts. We show that a local search with simpler operations than those used by P\'{a}l and Mahdian achieves the same approximation ratio of $8 + \epsilon$, and scaling technique can be used to improve it to $7.60 + \epsilon$. Secondly, we strengthen the operations used by P\'{a}l and Mahdian to improve the approximation guarantee to $7 + \epsilon$.

By: Vinayaka Dattatraya Pandit, Naveen Garg, Rohit Khandekar, Amit Kumar

Published in: RI03014 in 2003

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