The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2740 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.

翻译：平均情况分析面临的首要批评是，我们实际上并不了解真实世界输入的概率分布。因此，基于某种随机模型对算法进行分析，其实践性能意义甚微。这一批评的核心在于质疑外部有效性的存在，即假定算法在相对简单和清晰的模型上的表现无法推广至真实世界输入的实践性能。本文旨在系统研究外部有效性问题，迈出第一步探索。为此，我们评估了六种图算法在2740个稀疏真实世界网络上的性能，依据两个特性：异质性（度分布的方差）和局部性（边连接已接近顶点的趋势）。我们将其与具有不同局部性和异质性的生成网络上的性能进行比较。结果发现，在网络模型的理想化设定下，算法性能惊人地适用于真实世界网络。此外，异质性和局部性似乎是影响许多图算法性能的核心特性。