工程全动态$Δ$ -定位算法
Engineering Fully Dynamic $Δ$-Orientation Algorithms
摘要：
（完全）动态图算法是一种数据结构，它支持边插入、边删除，并回答特定于所考虑问题的某些查询。已经有很多关于图问题的动态算法的研究，这些图问题可以通过静态算法在多项式时间内求解。然而，虽然有大量的理论工作，有效的动态图算法，很多这些算法从来没有实现和经验评估。在这项工作中，我们考虑的完全动态的边缘定向问题，也称为完全动态的$Δ$ -定向问题，这是保持一个方向的无向图的边缘，使出度低。如果插入或删除边，则可能必须翻转某些边的方向，以避免顶点具有较大的出度。虽然已经有关于这个问题的动态版本的理论工作，但目前还没有可用的实验评估。在这项工作中，我们缩小了这一差距，并设计了一系列新的动态边缘定位算法以及当前文献中的算法。此外，我们评估这些算法在现实世界中的动态图。最好的算法，本文认为在质量方面，基于一个简单的广度优先搜索，计算最佳结果的情况下，超过90%，平均只有2.4%，比最佳解决方案。
英文摘要：
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers certain queries that are specific to the problem under consideration. There has been a lot of research on dynamic algorithms for graph problems that are solvable in polynomial time by a static algorithm. However, while there is a large body of theoretical work on efficient dynamic graph algorithms, a lot of these algorithms were never implemented and empirically evaluated. In this work, we consider the fully dynamic edge orientation problem, also called fully dynamic $Δ$-orientation problem, which is to maintain an orientation of the edges of an undirected graph such that the out-degree is low. If edges are inserted or deleted, one may have to flip the orientation of some edges in order to avoid vertices having a large out-degree. While there has been theoretical work on dynamic versions of this problem, currently there is no experimental evaluation available. In this work, we close this gap and engineer a range of new dynamic edge orientation algorithms as well as algorithms from the current literature. Moreover, we evaluate these algorithms on real-world dynamic graphs. The best algorithm considered in this paper in terms of quality, based on a simple breadth-first search, computes the optimum result on more than 90% of the instances and is on average only 2.4% worse than the optimum solution.
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