author tkwa Mon, 1 Aug 2016 20:38:16 +0000 (13:38 -0700) committer tkwa Mon, 1 Aug 2016 20:38:16 +0000 (13:38 -0700)
 doc/iotcloud.tex patch | blob | history

index 143791dfe6362e3fd3149d2fe464d382687b6f5f..250ddcf165b0c7eb011febd3268f9f88d5126b41 100644 (file)
@@ -6,6 +6,7 @@
\usepackage{graphicx}\r
\usepackage{mathrsfs}\r
\usepackage{algpseudocode}% http://ctan.org/pkg/algorithmicx\r
+\usepackage[all]{xy}\r
\newtheorem{theorem}{Theorem}\r
\newtheorem{prop}{Proposition}\r
\newtheorem{lem}{Lemma}\r
@@ -685,6 +686,14 @@ $\tuple{ck,\tuple{k, v}} \in KV_s \wedge \r \end{lem}\r \r +\begin{figure}[h]\r + \centering\r + \xymatrix{\r +\dots \ar[r] & q \ar[dr]_{J} \ar[r]^{K} & S_1 \ar[r] & S_2 \ar[rr] & & \dots \ar[r] & S_n = u \\\r +& & R_1 \ar[r] & R_2 \ar[r] & \dots \ar[r] & R_m = t}\r +\caption{By Lemma 2, receiving$t$before$u$is impossible.}\r +\end{figure}\r +\r \begin{lem} If two packets$t$and$u$, with$i(t) \le i(u)$, are received without errors by a client$C$, then$t$is in the path of$u$. \end{lem}\r \begin{proof}\r Assume that$t$is not in the path of$u$. Take$u$to be the packet of smallest index for which this occurs, and$t$be the packet with largest index for this$u$. We will prove that an error occurs upon receipt of$u\$.\r