Random walks on networks: Cumulative distribution of cover time

被引：10

作者：

Zlatanov, Nikola ^{[1
]}

Kocarev, Ljupco ^{[1
,2
]}

机构：

[1] Macedonian Acad Sci & Arts, Skopje 1000, North Macedonia

[2] Univ Calif San Diego, Inst Nonlinear Sci, La Jolla, CA 92093 USA

来源：

PHYSICAL REVIEW E | 2009年 / 80卷 / 04期

关键词：

graph theory; probability; random processes;

D O I：

10.1103/PhysRevE.80.041102

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a complete graph, a cycle graph, and a path graph. An accurate approximation for the cover time distribution, with computational complexity of O(2n), is also presented. The approximation is numerically tested only for graphs with n < 1000 nodes.

引用

页数：8

共 50 条

[31] A TIGHT LOWER-BOUND ON THE COVER TIME FOR RANDOM-WALKS ON GRAPHS
FEIGE, U
RANDOM STRUCTURES & ALGORITHMS, 1995, 6 (04) : 433 - 438
[32] Exceptional points of two-dimensional random walks at multiples of the cover time
Yoshihiro Abe
Marek Biskup
Probability Theory and Related Fields, 2022, 183 : 1 - 55
[33] Mean first return time for random walks on weighted networks
Jing, Xing-Li
Ling, Xiang
Long, Jiancheng
Shi, Qing
Hu, Mao-Bin
INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2015, 26 (06):
[34] Mean Hitting Time for Random Walks on a Class of Sparse Networks
Su, Jing
Wang, Xiaomin
Yao, Bing
ENTROPY, 2022, 24 (01)
[35] Expanded Koch networks: structure and trapping time of random walks
Hou, Baoyu
Zhang, Hongjuan
Liu, Li
EUROPEAN PHYSICAL JOURNAL B, 2013, 86 (04):
[36] First passage time distribution in random walks with absorbing boundaries
Nagar, A
Pradhan, P
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2003, 320 : 141 - 148
[37] Improving Partial Cover of Random Walks in large-scale Wireless Sensor Networks
Tzevelekas, Leonidas
Stavrakakis, Ioannis
2009 IEEE INTERNATIONAL SYMPOSIUM ON A WORLD OF WIRELESS, MOBILE AND MULTIMEDIA NETWORKS & WORKSHOPS, 2009, : 433 - 438
[38] Random walks and diffusion on networks
Masuda, Naoki
Porter, Mason A.
Lambiotte, Renaud
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2017, 716 : 1 - 58
[39] Random walks on sensor networks
Lima, Luisa
Barros, Joao
2007 5TH INTERNATIONAL SYMPOSIUM ON MODELING AND OPTIMIZATION IN MOBILE, AD HOC AND WIRELESS NETWORKS AND WORKSHOPS, VOLS 1-2, 2007, : 294 - 298
[40] Random Walks and Electric Networks
Nachmias, Asaf
PLANAR MAPS, RANDOM WALKS AND CIRCLE PACKING: ECOLE D'ETE DE PROBABILITES DE SAINT-FLOUR XLVIII - 2018, 2020, 2243 : 11 - 31

← 1 2 3 4 5 →