优先连接图的次线性随机访问生成器
Sublinear Random Access Generators for Preferential Attachment Graphs
AI总结：
针对 BA 优先连接图和随机递归树，论文提出按需即时生成的随机访问算法，使每查询的时间、空间和随机比特复杂度均为 polylog(n)。
摘要：
我们研究从图上的分布进行采样的问题，特别是当该分布由一个演化图模型定义时，并考察此类采样器的时间、空间和随机性复杂度。在标准方法中，整个图按照随机演化过程被随机选出、完整存储，随后对采样图的查询只需访问已存储的图来回答。这可能需要高得令人却步的时间、空间和随机比特量，尤其是在实际只发出少量查询的情况下。相反，我们提出根据查询即时生成图，从而使所需的时间、空间和随机比特量成为实际查询数量的函数。我们聚焦于两个随机图模型：Barabási-Albert 优先连接模型（BA-graphs）和随机递归树模型。我们为两个模型都给出了即时生成算法。以 1-1/poly(n) 的概率，每一个查询都在 polylog(n) 时间内得到回答，并且任意单个查询所导致的空间增量和消耗的随机比特数均为 polylog(n)，其中 n 表示图中的顶点数。我们的结果表明，尽管 BA 随机图模型由顺序过程定义，但对图节点的高效随机访问仍是可能的。除概念性贡献外，随机图的高效即时生成还可作为一种工具，用于在大型 BA-graphs 上高效模拟次线性算法，并高效估计这些算法在此类图上的性能。
英文摘要：
We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space and randomness complexities of such samplers. In the standard approach, the whole graph is chosen randomly according to the randomized evolving process, stored in full, and then queries on the sampled graph are answered by simply accessing the stored graph. This may require prohibitive amounts of time, space and random bits, especially when only a small number of queries are actually issued. Instead, we propose to generate the graph on-the-fly, in response to queries, and therefore to require amounts of time, space, and random bits which are a function of the actual number of queries. We focus on two random graph models: the Barab{á}si-Albert Preferential Attachment model (BA-graphs) and the random recursive tree model. We give on-the-fly generation algorithms for both models. With probability $1-1/\mbox{poly}(n)$, each and every query is answered in $\mbox{polylog}(n)$ time, and the increase in space and the number of random bits consumed by any single query are both $\mbox{polylog}(n)$, where $n$ denotes the number of vertices in the graph. Our results show that, although the BA random graph model is defined by a sequential process, efficient random access to the graph's nodes is possible. In addition to the conceptual contribution, efficient on-the-fly generation of random graphs can serve as a tool for the efficient simulation of sublinear algorithms over large BA-graphs, and the efficient estimation of their performance on such graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
