Exploration of the T-Interval-Connected Dynamic Graphs: the Case of the Ring
Exploration of the T-Interval-Connected Dynamic Graphs: the Case of the Ring
复制标题
T-区间连通动态图的探索：环的情况
DOI：
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发表时间：
2013
影响因子：
0.5
通讯作者：
A. Wade
中科院分区：
文献类型：
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作者：
D. Ilcinkas;A. Wade
在本文中，我们从移动实体（代理）（更确切地说，是t-的图形）研究了T-interval连接的动态图。间隔连接（t≥1），如果在连续的时间步长的每个窗口中都存在一个连接的跨度子图（始终存在），则在此期间引入了连接稳定性的属性。 Kuhn，Lynch和Oshman（Kuhn等人14）（Stoc 2010）。 t -θ（1）时间单元，如果代理知道图形的动力学，而n+nmax {1，t -1}（δ -1）±θ（δ）±θ（δ）documentClass [12pt] {minimal} usepackage {amsmath} usepackage {asysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {upgreek} setLength {oddSideMargin} { - 69pt} egin {document} $ n+ n+ frac {n} n} delta）$ end {document}时间单位否则，其中δ是两个成功的边缘外观之间的最大时间。
In this paper, we study the T-interval-connected dynamic graphs from the point of view of the time necessary and sufficient for their exploration by a mobile entity (agent). A dynamic graph (more precisely, an evolving graph) is T-interval-connected (T ≥ 1) if, for every window of T consecutive time steps, there exists a connected spanning subgraph that is stable (always present) during this period. This property of connection stability over time was introduced by Kuhn, Lynch and Oshman (Kuhn et al. 14) (STOC 2010). We focus on the case when the underlying graph is a ring of size n, and we show that the worst-case time complexity for the exploration problem is 2n − T − Θ(1) time units if the agent knows the dynamics of the graph, and n+nmax{1,T−1}(δ−1)±Θ(δ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$n+ frac {n}{max {1, T-1} } (delta -1) pm {Theta }(delta )$end{document} time units otherwise, where δ is the maximum time between two successive appearances of an edge.