圆图的不经意堆叠与MAX $k$ - CUT
Oblivious Stacking and MAX $k$-CUT for Circle Graphs
摘要：
堆垛是物流中的一个重要过程。要堆放的物品的一些显著的例子是钢堆场中的钢筋或钢板或集装箱码头或船上的集装箱。如果两个项目的存储时间间隔重叠，我们说这两个项目是冲突的，在这种情况下，其中一个项目需要重新处理，如果项目存储在相同的后进先出存储位置。我们考虑使用$k$ LIFO位置的堆叠项目的问题，共享一个位置的项目之间的冲突数量最少。我们提出了一个非常简单的在线堆叠算法，是不经意的存储时间间隔和存储位置的所有其他项目时，它挑选一个存储位置的项目。分配相同的存储位置的两个冲突的项目的风险被证明是顺序$1/k^2$下的项目的存储时间间隔的分布的温和的假设。直觉上，在不经意的设置中随机均匀地选择一个存储位置似乎是很自然的，这意味着$1/k$的风险，因此我们的算法的风险出奇地低。我们的结果也可以表示的上下文中的最大$k$ -切问题的圆图。结果表明，平均而言，圆图具有相对较大的$k$ -割相比，总的边缘数。
英文摘要：
Stacking is an important process within logistics. Some notable examples of items to be stacked are steel bars or steel plates in a steel yard or containers in a container terminal or on a ship. We say that two items are conflicting if their storage time intervals overlap in which case one of the items needs to be rehandled if the items are stored at the same LIFO storage location. We consider the problem of stacking items using $k$ LIFO locations with a minimum number of conflicts between items sharing a location. We present an extremely simple online stacking algorithm that is oblivious to the storage time intervals and storage locations of all other items when it picks a storage location for an item. The risk of assigning the same storage location to two conflicting items is proved to be of the order $1/k^2$ under mild assumptions on the distribution of the storage time intervals for the items. Intuitively, it seems natural to pick a storage location uniformly at random in the oblivious setting implying a risk of $1/k$ so the risk for our algorithm is surprisingly low. Our results can also be expressed within the context of the MAX $k$-CUT problem for circle graphs. The results indicate that circle graphs on average have relatively big $k$-cuts compared to the total number of edges.
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