The paper studies the problem of Public Event Scheduling with Busy Agents (PESBA), where multiple public events need to be scheduled to coordinate the availability of multiple agents. Each agent has a set of jobs that must be preemptively processed, and the agents want to attend as many events as possible.
The key highlights and insights are:
The PESBA problem is shown to be NP-hard, even in the case where there is only one agent and the agent has only two rigid jobs.
For the case where the whole timeline is polynomially bounded, a natural greedy algorithm is proposed that achieves a 1/2-approximation. This algorithm works by having agents vote on the best positions for each unscheduled event, and then selecting the event and position that maximizes the total agreement.
The paper also shows that the agreement function is submodular, and that it can be viewed as the rank function of a matroid. This allows the greedy algorithm to be extended to the general case with an arbitrary timeline, achieving a 1/(α+1)-approximation, where α is the approximation ratio of the algorithm for the one-event instance.
An optimal algorithm is provided for the one-event instance, which implies a 1/2-approximate algorithm for the general case.
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by Bo Li,Lijun ... om arxiv.org 04-19-2024
https://arxiv.org/pdf/2404.11879.pdfDiepere vragen