The winter road maintenance arc-routing is recognized as a notoriously hard problem not only from the algorithmic point of view. This paper lays down foundations of theoretical understanding of our new winter road maintenance optimization for the Plzeň region of the Czech Republic which has been implemented by the regional authorities since the winter of 2019–20. Our approach is not, contrary to most of existing work, based on the integer and linear programming machinery. We concentrate on studying arc-routing on trees. This is practical since routes of single vehicles can be well represented by trees, and allows algorithms and complementary hardness results. We then extend the approach to the bounded tree width graphs. This leads to considering planar graphs which well abstract the realistic road networks. We formalize important aspects of the winter road maintenance problem which were not formalized before, e.g., public complaints. The number of complaints from public against the winter road maintenance is a quantitative measure of the quality of the service which is focused on, e.g., in media or in election campaigns. A fear of ’complaints’ is a fact every optimizer must deal with. Hence, a formal model of public complaints and its inclusion in the optimization is vital. Our formalization of the winter road maintenance is robust in the sense that it relates to well-known extensively studied concepts of discrete mathematics like graph cutting and splitting of necklaces.

不仅从算法的角度来看，冬季道路养护电弧路由被认为是一个众所周知的难题。本文为我们针对捷克共和国比尔森地区的冬季道路养护新优化奠定了理论理解的基础，该优化已于2019-20年冬季开始由地区政府实施。与大多数现有工作相反，我们的方法不是基于整数和线性编程机制。我们专注于研究树木上的弧线布线。这是可行的，因为单个车辆的路线可以用树很好地表示，并允许算法和互补的硬度结果。然后，我们将方法扩展到有界树宽图。这导致需要考虑可以很好地抽象现实道路网络的平面图。我们将冬季养路问题的重要方面确定为正式形式，例如在公众投诉之前尚未正式确定的形式。公众对冬季道路养护的投诉数量是对服务质量的定量衡量，例如，在媒体或竞选活动中，这种质量衡量是重点。担心“投诉”是每个优化器必须处理的事实。因此，建立公众投诉的正式模型并将其包含在优化中至关重要。我们对冬季道路维护的形式化是有说服力的，因为它涉及到众所周知的广泛研究的离散数学概念，例如图形切割和项链拆分。公众对冬季道路养护的投诉数量是对服务质量的定量衡量，例如，在媒体或竞选活动中，这种质量衡量是重点。担心“投诉”是每个优化器必须处理的事实。因此，建立公众投诉的正式模型并将其包含在优化中至关重要。我们对冬季道路维护的形式化是有说服力的，因为它涉及到众所周知的广泛研究的离散数学概念，例如图形切割和项链拆分。公众对冬季道路养护的投诉数量是对服务质量的定量衡量，例如，在媒体或竞选活动中，这种质量衡量是重点。担心“投诉”是每个优化器必须处理的事实。因此，建立公众投诉的正式模型并将其包含在优化中至关重要。我们对冬季道路维护的形式化是有说服力的，因为它涉及到众所周知的广泛研究的离散数学概念，例如图形切割和项链拆分。