[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 04:06:59

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

Log message:
        More formal definitions

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/misc/hemppah-progradu/masterthesis.tex.diff?tr1=1.161&tr2=1.162&r1=text&r2=text

Patches:
Index: gzz/Documentation/misc/hemppah-progradu/masterthesis.tex
diff -u gzz/Documentation/misc/hemppah-progradu/masterthesis.tex:1.161 
gzz/Documentation/misc/hemppah-progradu/masterthesis.tex:1.162
--- gzz/Documentation/misc/hemppah-progradu/masterthesis.tex:1.161      Thu Mar 
20 03:43:18 2003
+++ gzz/Documentation/misc/hemppah-progradu/masterthesis.tex    Thu Mar 20 
04:06:59 2003
@@ -277,15 +277,15 @@
 \subsection{Sketch of a formal definition}
 
 In this subsection we formalize loosely structured overlay's main components. 
This
-model is based on original Gnutella overlay network with power-law 
improvements.
+model is based on original Gnutella overlay network with scale-free 
improvements.
 
 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 $p = \delta(s)$. 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, $si = 
\gamma(\delta(s))$
-and $\forall$ regular peer $p$, and has a index of regular
-peer's content, specifically $sp$, $P$ = \{$p \in P: \exists sp$, 
+is $P$ = \{$p \in P: \exists neighbor$, which is randomly chosen from $P$\}. 
+Summary index maintains indices of other peers, $si = \gamma(\delta(s))$.
+Then, $\forall$ regular peer $p$, there is a super peer, $sp$, and it has a 
index of 
+regular peer's content $P$ = \{$p \in P: \exists sp$, 
 where $sp$ = $\delta(\gamma(\delta(s))) \wedge (p = \delta(s))$\}
 
 \section{Tightly structured}
@@ -457,12 +457,11 @@
 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 $p = \delta(s)$. 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 $\zeta: I \longmapsto IS$, 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 $IS$ = \{$ip 
\in IS: 
-\exists s \in S$, $ip = \zeta(\iota(s)) \wedge (\delta(s) = p)$\}.
+is defined as $i = \iota(s)$. Coordinate point is defined as $ip = 
\zeta(\iota(s))$.
+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 $\zeta: I 
\longmapsto IS$,  
+which maps data items, expressed by an identifier to coordinate point $ip$ in 
$(IS,d)$. Peer's $p$ 
+resources are mapped onto a set $IS$ = \{$ip \in IS: \exists s \in S$, $ip = 
\zeta(\iota(s)) \wedge (\delta(s) = p)$\}.
 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 $(IS,d)$\}.