TY - GEN

T1 - Almost Tight Bounds for Online Facility Location in the Random-Order Model

AU - Kaplan, Haim

AU - Naori, David

AU - Raz, Danny

N1 - Publisher Copyright:
Copyright © 2023 by SIAM.

PY - 2023

Y1 - 2023

N2 - We study the online facility location problem with uniform facility costs in the random-order model. Meyerson's algorithm [FOCS'01] is arguably the most natural and simple online algorithm for the problem with several advantages and appealing properties. Its analysis in the random-order model is one of the cornerstones of random-order analysis beyond the secretary problem. Meyerson's algorithm was shown to be (asymptotically) optimal in the standard worst-case adversarial-order model and 8-competitive in the random order model. While this bound in the random-order model is the long-standing state-of-the-art, it is not known to be tight, and the true competitive-ratio of Meyerson's algorithm remained an open question for more than two decades. We resolve this question and prove tight bounds on the competitive-ratio of Meyerson's algorithm in the random-order model, showing that it is exactly 4-competitive. Following our tight analysis, we introduce a generic parameterized version of Meyerson's algorithm that retains all the advantages of the original version. We show that the best algorithm in this family is exactly 3-competitive. On the other hand, we show that no online algorithm for this problem can achieve a competitive-ratio better than 2. Finally, we prove that the algorithms in this family are robust to partial adversarial arrival orders.

AB - We study the online facility location problem with uniform facility costs in the random-order model. Meyerson's algorithm [FOCS'01] is arguably the most natural and simple online algorithm for the problem with several advantages and appealing properties. Its analysis in the random-order model is one of the cornerstones of random-order analysis beyond the secretary problem. Meyerson's algorithm was shown to be (asymptotically) optimal in the standard worst-case adversarial-order model and 8-competitive in the random order model. While this bound in the random-order model is the long-standing state-of-the-art, it is not known to be tight, and the true competitive-ratio of Meyerson's algorithm remained an open question for more than two decades. We resolve this question and prove tight bounds on the competitive-ratio of Meyerson's algorithm in the random-order model, showing that it is exactly 4-competitive. Following our tight analysis, we introduce a generic parameterized version of Meyerson's algorithm that retains all the advantages of the original version. We show that the best algorithm in this family is exactly 3-competitive. On the other hand, we show that no online algorithm for this problem can achieve a competitive-ratio better than 2. Finally, we prove that the algorithms in this family are robust to partial adversarial arrival orders.

UR - http://www.scopus.com/inward/record.url?scp=85154056165&partnerID=8YFLogxK

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AN - SCOPUS:85154056165

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1523

EP - 1544

BT - 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023

PB - Association for Computing Machinery

T2 - 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023

Y2 - 22 January 2023 through 25 January 2023

ER -