For personalized two-value instances, a deterministic online algorithm maintains a tight 1/(2n-1)-maximin-share allocation at every step, and limited foresight yields EF1 every n steps.
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Online Fair Division for Personalized $2$-Value Instances
For personalized two-value instances, a deterministic online algorithm maintains a tight 1/(2n-1)-maximin-share allocation at every step, and limited foresight yields EF1 every n steps.