We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes the computational cost in terms of a parameter k that characterizes the computational power provided by limited local computing resources. We develop new algorithmic techniques that implement algorithms for solving well-known computational problems on the proposed model. In particular, we present an algorithm that finds a k-matching in a general unweighted graph in time O(N + k^{2.5}) and an algorithm that constructs a maximum weighted k-matching in a general weighted graph in time O(N + k^3 log k). Both algorithms have their space complexity bounded by O(k^2).

中文翻译：

---

本地资源有限的线性时间参数化算法

我们提出了一种新的（理论）计算模型，用于研究计算资源有限的海量数据处理。我们的模型根据数据大小 N 来衡量读取超大数据集的复杂性，并根据参数 k 分析计算成本，该参数表征了有限本地计算资源提供的计算能力。我们开发了新的算法技术，这些技术实现了解决所提出模型上众所周知的计算问题的算法。特别地，我们提出了一种在时间为 O(N + k^{2.5}) 的一般未加权图中找到 k-匹配的算法，以及在时间为 O( N + k^3 log k)。两种算法的空间复杂度都以 O(k^2) 为界。