Majumdar Satya N
Laboratoire de Physique Théorique (FER 2603 du CNRS), Université Paul Sabatier, 31062 Toulouse Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 2):026103. doi: 10.1103/PhysRevE.68.026103. Epub 2003 Aug 5.
We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion-limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely, the digital search tree problem in data structures and the Lempel-Ziv algorithm for data compression. The statistics of the number of particles studied here is related to the statistics of height in digital search trees which, in turn, is related to the statistics of the length of the longest word formed by the Lempel-Ziv algorithm. Implications of our results to these computer science problems are pointed out.
我们采用行波前沿方法，来推导凯莱树上一类有向扩散限制聚集模型中粒子数统计量的精确渐近结果。我们指出，这些模型的某些方面与计算机科学中的两个不同问题紧密相关，即数据结构中的数字搜索树问题以及用于数据压缩的莱姆尔 - 齐夫算法。这里所研究的粒子数统计量与数字搜索树的高度统计量相关，而数字搜索树的高度统计量又与莱姆尔 - 齐夫算法所形成的最长单词长度的统计量相关。我们还指出了我们的结果对这些计算机科学问题的影响。
