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\subsection{Sketch of a formal definition} |
\subsection{Sketch of a formal definition} |
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In this subsection we formalize loosely structured overlay's main components. This |
In this subsection we formalize loosely structured overlay's main components. This |
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model is based on original Gnutella overlay network with power-law improvements. |
model is based on original Gnutella overlay network with scale-free improvements. |
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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 |
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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, |
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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 |
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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 $P$\}. |
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\emph{Super peer} is a peer, which hosts the indices of other peers, $si = \gamma(\delta(s))$ |
Summary index maintains indices of other peers, $si = \gamma(\delta(s))$. |
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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 |
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peer's content, specifically $sp$, $P$ = \{$p \in P: \exists sp$, |
regular peer's content $P$ = \{$p \in P: \exists sp$, |
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where $sp$ = $\delta(\gamma(\delta(s))) \wedge (p = \delta(s))$\} |
where $sp$ = $\delta(\gamma(\delta(s))) \wedge (p = \delta(s))$\} |
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\section{Tightly structured} |
\section{Tightly structured} |
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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. |
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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, $\forall s \in S$, |
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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 |
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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 $ip = \zeta(\iota(s))$. |
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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 |
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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 $\zeta: I \longmapsto IS$, |
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$ip = \zeta(\iota(s))$, 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 $p$ |
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point $ip$ in $(IS,d)$. Peer's p resources are mapped onto a set $IS$ = \{$ip \in IS: |
resources are mapped onto a set $IS$ = \{$ip \in IS: \exists s \in S$, $ip = \zeta(\iota(s)) \wedge (\delta(s) = p)$\}. |
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\exists s \in S$, $ip = \zeta(\iota(s)) \wedge (\delta(s) = p)$\}. |
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Every $p$ has neighbor(s), named as $p_n$, $P$ = \{$p \in P: \exists p_n$, |
Every $p$ has neighbor(s), named as $p_n$, $P$ = \{$p \in P: \exists p_n$, |
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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 $(IS,d)$\}. |
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