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Title: Improved Bi-Point Rounding Algorithms and a Golden Barrier for k-median
The current-best approximation algorithms for k-median rely on first obtaining a structured fractional solution known as a bi-point solution, and then rounding it to an integer solution. We improve this second step by unifying and refining previous approaches. We describe a hierarchy of increasingly-complex partitioning schemes for the facilities, along with corresponding sets of algorithms and factor-revealing non-linear programs. We prove that the third layer of this hierarchy is a 2.613-approximation, improving upon the current-best ratio of 2.675, while no layer can be proved better than 2.588 under the proposed analysis. On the negative side, we give a family of bi-point solutions which cannot be approximated better than the square root of the golden ratio, even if allowed to open k + o(k) facilities. This gives a barrier to current approaches for obtaining an approximation better than approximately 2.544. Altogether we reduce the approximation gap of bi-point solutions by two thirds.  more » « less
Award ID(s):
1918749
PAR ID:
10404310
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA)
Page Range / eLocation ID:
987-1011
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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