Randomising the length of the first step will improve on the constant factor by about 2. Similar analysis to the non-adversarial case, and with the same ETA I just added to my earlier comment.
Ah yes, OK, essentially the same randomization helps against an adversary when you’re growing exponentially as when you’re growing only linearly. Fair enough.
Randomising the length of the first step will improve on the constant factor by about 2. Similar analysis to the non-adversarial case, and with the same ETA I just added to my earlier comment.
If you make the run lengths increase exponentially instead of linearly then you get O(k) unconditionally.
I know. I was improving the constant factor.
Ah yes, OK, essentially the same randomization helps against an adversary when you’re growing exponentially as when you’re growing only linearly. Fair enough.