图上代数流言的界
Bounds for Algebraic Gossip on Graphs
摘要：
我们研究了网络编码的流言算法的停止时间。我们分析代数八卦（即，随机线性编码），并考虑三个八卦算法的信息传播拉，推，和交换。代数流言的停止时间对于完全图是线性的，但是对于一般图确定一个紧的上界或下界的问题仍然是开放的。我们在解决这个问题上迈出了重要的一步，并证明了任何大小为n的图的代数八卦是O（D*n），其中D是图的最大程度。这导致有界度图的Theta（n）的紧界和一般图的O（n^2）的上界。我们通过提供一个停时为Omega（n^2）的图的例子来证明后一个界是紧的。我们的证明使用一种新的方法，依赖于杰克逊的排队定理来分析网络编码的停止时间，这种技术可能会成为有用的未来的研究。
英文摘要：
We study the stopping times of gossip algorithms for network coding. We analyze algebraic gossip (i.e., random linear coding) and consider three gossip algorithms for information spreading Pull, Push, and Exchange. The stopping time of algebraic gossip is known to be linear for the complete graph, but the question of determining a tight upper bound or lower bounds for general graphs is still open. We take a major step in solving this question, and prove that algebraic gossip on any graph of size n is O(D*n) where D is the maximum degree of the graph. This leads to a tight bound of Theta(n) for bounded degree graphs and an upper bound of O(n^2) for general graphs. We show that the latter bound is tight by providing an example of a graph with a stopping time of Omega(n^2). Our proofs use a novel method that relies on Jackson's queuing theorem to analyze the stopping time of network coding; this technique is likely to become useful for future research.
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。
