/[gzz]/gzz/Documentation/misc/hemppah-progradu/masterthesis.tex
ViewVC logotype

Diff of /gzz/Documentation/misc/hemppah-progradu/masterthesis.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Patch Patch

revision 1.161 by hemppah, Thu Mar 20 08:43:18 2003 UTC revision 1.162 by hemppah, Thu Mar 20 09:06:59 2003 UTC
# Line 277  to improve data lookup of loosely struct Line 277  to improve data lookup of loosely struct
277  \subsection{Sketch of a formal definition}  \subsection{Sketch of a formal definition}
278    
279  In this subsection we formalize loosely structured overlay's main components. This  In this subsection we formalize loosely structured overlay's main components. This
280  model is based on original Gnutella overlay network with power-law improvements.  model is based on original Gnutella overlay network with scale-free improvements.
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 $p = \delta(s)$. 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, $si = \gamma(\delta(s))$  Summary index maintains indices of other peers, $si = \gamma(\delta(s))$.
287  and $\forall$ regular peer $p$, and has a index of regular  Then, $\forall$ regular peer $p$, there is a super peer, $sp$, and it has a index of
288  peer's content, specifically $sp$, $P$ = \{$p \in P: \exists sp$,  regular peer's content $P$ = \{$p \in P: \exists sp$,
289  where $sp$ = $\delta(\gamma(\delta(s))) \wedge (p = \delta(s))$\}  where $sp$ = $\delta(\gamma(\delta(s))) \wedge (p = \delta(s))$\}
290    
291  \section{Tightly structured}  \section{Tightly structured}
# Line 457  Let $S$ be the aggregate of all services Line 457  Let $S$ be the aggregate of all services
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 $p = \delta(s)$. Service's identifier  there is a provider of the service, expressed as $p = \delta(s)$. Service's identifier
460  is defined as $i = \iota(s)$. Metric space is defined as a pair $(IS,d)$, where $d$  is defined as $i = \iota(s)$. Coordinate point is defined as $ip = \zeta(\iota(s))$.
461  is the distance between two coordinate points $ip_i$, $ip_j$ in $IS$ space. Mapping  Metric space is defined as a pair $(IS,d)$, where $d$ is the distance between two coordinate
462  function is defined as $\zeta: I \longmapsto IS$, and coordinate point as  points $ip_i$, $ip_j$ in $IS$ space. Mapping function is defined as $\zeta: I \longmapsto IS$,  
463  $ip = \zeta(\iota(s))$, which maps data items, expressed by an identifier to coordinate  which maps data items, expressed by an identifier to coordinate point $ip$ in $(IS,d)$. Peer's $p$
464  point $ip$ in $(IS,d)$. Peer's p resources are mapped onto a set $IS$ = \{$ip \in IS:  resources are mapped onto a set $IS$ = \{$ip \in IS: \exists s \in S$, $ip = \zeta(\iota(s)) \wedge (\delta(s) = p)$\}.
 \exists s \in S$, $ip = \zeta(\iota(s)) \wedge (\delta(s) = p)$\}.  
465  Every $p$ has neighbor(s), named as $p_n$, $P$ = \{$p \in P: \exists p_n$,  Every $p$ has neighbor(s), named as $p_n$, $P$ = \{$p \in P: \exists p_n$,
466  where $\theta(p,p_n) = ''close''$, where $''close''$ is small difference $d$ in $(IS,d)$\}.  where $\theta(p,p_n) = ''close''$, where $''close''$ is small difference $d$ in $(IS,d)$\}.
467    

Legend:
Removed from v.1.161  
changed lines
  Added in v.1.162

savannah-hackers-public@gnu.org
ViewVC Help
Powered by ViewVC 1.1.26