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revision 1.158 by hemppah, Wed Mar 19 09:56:45 2003 UTC revision 1.159 by hemppah, Thu Mar 20 08:14:20 2003 UTC
# Line 281  model is based on original Gnutella over Line 281  model is based on original Gnutella over
281    
282  Let $S$ be the aggregate of all services $s$ in system. Let $P$ be the aggregate of  Let $S$ be the aggregate of all services $s$ in system. Let $P$ be the aggregate of
283  all peers $p$ in system. Then, $\forall s \in S$, there is a provider of the service,  all peers $p$ in system. Then, $\forall s \in S$, there is a provider of the service,
284  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
285  is $P$ = \{$p \in P: \exists neighbor$, which is randomly chosen from $P$\}.  is $P$ = \{$p \in P: \exists neighbor$, which is randomly chosen from $P$\}.
286  \emph{Super peer} is a peer, which hosts the indices of other peers, $si = summaryindex(provider(s))$  \emph{Super peer} is a peer, which hosts the indices of other peers, $si = \gamma(\delta(s))$
287  and $\forall$ regular peer $p$, there is super peer, which has has a index of regular  and $\forall$ regular peer $p$, and has a index of regular
288  peer's content, specifically $sp$, $P$ = \{$p \in P: \exists sp$,  peer's content, specifically $sp$, $P$ = \{$p \in P: \exists sp$,
289  where $sp$ = $provider(summaryindex(provider(s))) \wedge (p = provider(s))$\}  where $sp$ = $\delta(\gamma(\delta(s))) \wedge (p = \delta(s))$\}
290    
291    
292  \section{Tightly structured}  \section{Tightly structured}
# Line 326  process of data to key mapping in a tigh Line 326  process of data to key mapping in a tigh
326    
327  \begin{figure}  \begin{figure}
328  \centering  \centering
329  \includegraphics[width=12cm, height=6cm]{structured_overlay.eps}  \includegraphics[width=12cm, height=7cm]{structured_overlay_new.eps}
330  \caption{Principal idea of tightly structured overlays.}  \caption{Principal idea of tightly structured overlays.}
331  \label{fig:structured_hashing}  \label{fig:structured_hashing}
332  \end{figure}  \end{figure}
# Line 456  identifiers, identifier space and mappin Line 456  identifiers, identifier space and mappin
456  Let $S$ be the aggregate of all services $s$ in the system. Let $P$ be the aggregate of  Let $S$ be the aggregate of all services $s$ in the system. Let $P$ be the aggregate of
457  all peers $p$ in system. Let $I$ be the aggregate of all identifiers $i$ in system.  all peers $p$ in system. Let $I$ be the aggregate of all identifiers $i$ in system.
458  Let $IS$ be the aggregate of all identifier points $ip$ in system. Then, $\forall s \in S$,  Let $IS$ be the aggregate of all identifier points $ip$ in system. Then, $\forall s \in S$,
459  there is a provider of the service, expressed as $p = provider(s)$. Service's identifier  there is a provider of the service, expressed as $p = \delta(s)$. Service's identifier
460  is defined as $i = identifier(s)$. Metric space is defined as a pair $(IS,d)$, where $d$  is defined as $i = \iota(s)$. Metric space is defined as a pair $(IS,d)$, where $d$
461  is the distance between two coordinate points $ip_i$, $ip_j$ in $IS$ space. Mapping  is the distance between two coordinate points $ip_i$, $ip_j$ in $IS$ space. Mapping
462  function is defined as $map: I \longmapsto IS$, and coordinate point as  function is defined as $\zeta: I \longmapsto IS$, and coordinate point as
463  $ip = map(identifier(s))$, which maps data items, expressed by an identifier to coordinate  $ip = \zeta(\iota(s))$, which maps data items, expressed by an identifier to coordinate
464  point $ip$ in $(IS,d)$. Peer's p resources are mapped onto a set $IS$ = \{$ip \in IS:  point $ip$ in $(IS,d)$. Peer's p resources are mapped onto a set $IS$ = \{$ip \in IS:
465  \exists s \in S$, $ip = map(identifier(s)) \wedge (provider(s) = p)$\}.  \exists s \in S$, $ip = \zeta(\iota(s)) \wedge (\delta(s) = p)$\}.
466  Every $p$ has neighbor(s), named as $neighbor$, which are $P$ = \{$p \in P: \exists neighbor$,  Every $p$ has neighbor(s), named as $p_n$, $P$ = \{$p \in P: \exists p_n$,
467  where $difference(p,neighbor) = ''close''$, where $''close''$ is small difference $d$ in $(IS,d)$\}.  where $\theta(p,p_n) = ''close''$, where $''close''$ is small difference $d$ in $(IS,d)$\}.
468    
469    
470  \section{Summary}  \section{Summary}

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