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 From: Hermanni Hyytiälä Subject: [Gzz-commits] gzz/Documentation/misc/hemppah-progradu mastert... Date: Thu, 20 Mar 2003 04:06:59 -0500

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Hermanni Hyytiälä <address@hidden>      03/03/20 04:06:59

Modified files:

Log message:
More formal definitions

CVSWeb URLs:

Patches:
20 03:43:18 2003
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 $(IS,d)$\}.