The deterministic competitive ratio of the Parking Permit Problem is exactly K; the randomized ratio is at most ln K + ln ln K + O(1) and at least ln K + ln ln K + o(1).
Karlin and Mark S
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Primal-Dual Online Algorithms for the Parking Permit Problem
The deterministic competitive ratio of the Parking Permit Problem is exactly K; the randomized ratio is at most ln K + ln ln K + O(1) and at least ln K + ln ln K + o(1).