[Gzz-commits] gzz/Documentation/misc/hemppah-progradu mastert...

[Hermanni Hyytiälä]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Hermanni Hyytiälä <address@hidden>      03/03/20 03:14:20

Modified files:
        Documentation/misc/hemppah-progradu: masterthesis.tex 

Log message:
        Updates to formal definitions

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/misc/hemppah-progradu/masterthesis.tex.diff?tr1=1.158&tr2=1.159&r1=text&r2=text

Patches:
Index: gzz/Documentation/misc/hemppah-progradu/masterthesis.tex
diff -u gzz/Documentation/misc/hemppah-progradu/masterthesis.tex:1.158 
gzz/Documentation/misc/hemppah-progradu/masterthesis.tex:1.159
--- gzz/Documentation/misc/hemppah-progradu/masterthesis.tex:1.158      Wed Mar 
19 04:56:45 2003
+++ gzz/Documentation/misc/hemppah-progradu/masterthesis.tex    Thu Mar 20 
03:14:20 2003
@@ -281,12 +281,12 @@
 
 Let $S$ be the aggregate of all services $s$ in system. Let $P$ be the 
aggregate of 
 all peers $p$ in system. Then, $\forall s \in S$, there is a provider of the 
service, 
-expressed as $p = provider(s)$. Every $p$ has neighbor(s), named as $p_n$, 
which 
+expressed as $p = \delta(s)$. Every $p$ has neighbor(s), named as $p_n$, which 
 is $P$ = \{$p \in P: \exists neighbor$, which is randomly chosen from $P$\}.
-\emph{Super peer} is a peer, which hosts the indices of other peers, $si = 
summaryindex(provider(s))$
-and $\forall$ regular peer $p$, there is super peer, which has has a index of 
regular
+\emph{Super peer} is a peer, which hosts the indices of other peers, $si = 
\gamma(\delta(s))$
+and $\forall$ regular peer $p$, and has a index of regular
 peer's content, specifically $sp$, $P$ = \{$p \in P: \exists sp$, 
-where $sp$ = $provider(summaryindex(provider(s))) \wedge (p = provider(s))$\}
+where $sp$ = $\delta(\gamma(\delta(s))) \wedge (p = \delta(s))$\}
 
 
 \section{Tightly structured}
@@ -326,7 +326,7 @@
 
 \begin{figure}
 \centering
-\includegraphics[width=12cm, height=6cm]{structured_overlay.eps}
+\includegraphics[width=12cm, height=7cm]{structured_overlay_new.eps}
 \caption{Principal idea of tightly structured overlays.}
 \label{fig:structured_hashing}
 \end{figure}
@@ -456,15 +456,15 @@
 Let $S$ be the aggregate of all services $s$ in the system. Let $P$ be the 
aggregate of 
 all peers $p$ in system. Let $I$ be the aggregate of all identifiers $i$ in 
system. 
 Let $IS$ be the aggregate of all identifier points $ip$ in system. Then, 
$\forall s \in S$, 
-there is a provider of the service, expressed as $p = provider(s)$. Service's 
identifier 
-is defined as $i = identifier(s)$. Metric space is defined as a pair $(IS,d)$, 
where $d$
+there is a provider of the service, expressed as $p = \delta(s)$. Service's 
identifier 
+is defined as $i = \iota(s)$. Metric space is defined as a pair $(IS,d)$, 
where $d$
 is the distance between two coordinate points $ip_i$, $ip_j$ in $IS$ space. 
Mapping 
-function is defined as $map: I \longmapsto IS$, and coordinate point as 
-$ip = map(identifier(s))$, which maps data items, expressed by an identifier 
to coordinate 
+function is defined as $\zeta: I \longmapsto IS$, and coordinate point as 
+$ip = \zeta(\iota(s))$, which maps data items, expressed by an identifier to 
coordinate 
 point $ip$ in $(IS,d)$. Peer's p resources are mapped onto a set $IS$ = \{$ip 
\in IS: 
-\exists s \in S$, $ip = map(identifier(s)) \wedge (provider(s) = p)$\}.
-Every $p$ has neighbor(s), named as $neighbor$, which are $P$ = \{$p \in P: 
\exists neighbor$, 
-where $difference(p,neighbor) = ''close''$, where $''close''$ is small 
difference $d$ in $(IS,d)$\}.
+\exists s \in S$, $ip = \zeta(\iota(s)) \wedge (\delta(s) = p)$\}.
+Every $p$ has neighbor(s), named as $p_n$, $P$ = \{$p \in P: \exists p_n$, 
+where $\theta(p,p_n) = ''close''$, where $''close''$ is small difference $d$ 
in $(IS,d)$\}.
 
 
 \section{Summary}