The optimality of the online greedy algorithm in carpool and chairman assignment problems

We study several classes of related scheduling problems including the carpool problem, its generalization to arbitrary inputs and the chairman assignment problem. We derive both lower and upper bounds for online algorithms solving these problems. We show that the greedy algorithm is optimal among online algorithms for the chairman assignment problem and the generalized carpool problem. We also consider geometric versions of these problems and show how the bounds adapt to these cases.

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