无间隙无空缺医生排班的重叠最小化问题及通用名称查询

Hey there! Great question—this scheduling problem is most commonly referred to as the minimum overlap interval covering problem, a specialized variant of interval optimization problems.

Here’s a quick breakdown to confirm this matches your use case:

• Unlike classic interval scheduling problems (like maximizing non-overlapping shifts or covering a window with the fewest intervals), your priority is twofold:
  1. Ensure continuous coverage (no gaps where no doctor is on duty)
  2. Minimize the total overlapping time between the selected shifts
• In operational research contexts, it’s sometimes grouped under broader terms like "resource scheduling with minimal overlap," but "minimum overlap interval covering" is the most precise keyword for targeted searches.

Your approach to model this as a shortest path problem is spot-on! Framing each doctor’s shift as a node, with edge weights representing the overlap between consecutive shifts, lets you use shortest path algorithms to find the sequence of shifts that covers the required window with the least total overlap—this is a well-documented reduction for这类 problems.

To find reference materials, use the exact term "minimum overlap interval covering" in academic databases, operations research journals, or even technical blog posts focused on scheduling algorithms. You’ll find analyses of solution approaches, complexity proofs, and real-world applications similar to your hospital scheduling scenario.

内容的提问来源于stack exchange，提问作者Rikeijin