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Protocols for Secure Communication in Wireless Sensor Networks

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5.2. Rout<strong>in</strong>g on Spann<strong>in</strong>g Trees 135<br />

be adapted to ensure that a node is connected to the parent that is closest to the<br />

root.<br />

Each node ma<strong>in</strong>ta<strong>in</strong>s a data structure T <strong>for</strong> each spann<strong>in</strong>g tree, which holds<br />

the <strong>in</strong><strong>for</strong>mation required <strong>for</strong> rout<strong>in</strong>g. For a tree with identifier t, an entry T [t] is<br />

ma<strong>in</strong>ta<strong>in</strong>ed. Such an entry has the follow<strong>in</strong>g components:<br />

• parent – The parent node with<strong>in</strong> this tree (where the root is its own parent).<br />

• reach – A mapp<strong>in</strong>g from child identifiers to their covered address space.<br />

For a child c, T [t].reach(c) is a representation of the address space reachable<br />

through c. If a message is dest<strong>in</strong>ed to address d and d ∈ T [t].reach(c),<br />

node c may either be qualified to handle the message itself, or deliver it to<br />

a node closer to d.<br />

It is well possible that, dur<strong>in</strong>g tree construction, overlaps between children<br />

occur and part of the address space is covered by multiple children. This is due<br />

to the (possible) fuzz<strong>in</strong>ess of the ⊎ operator, which merges the address spaces<br />

of a node and its children. We will discuss the <strong>in</strong>efficiencies that may arise<br />

when <strong>in</strong>stantiat<strong>in</strong>g the rout<strong>in</strong>g framework with concrete schemes.<br />

5.2.3 Address<strong>in</strong>g on Spann<strong>in</strong>g Trees<br />

A critical aspect of tree-based rout<strong>in</strong>g is which type of address<strong>in</strong>g should be<br />

used. We discuss a canonical address<strong>in</strong>g scheme, which is useful only <strong>for</strong> a<br />

limited range of applications, and a more generally applicable geographical<br />

address<strong>in</strong>g scheme.<br />

Def<strong>in</strong>itions<br />

Generally, we can consider an abstract address space D. With each node u, a<br />

set<br />

coveru ⊂ D<br />

is associated that comprises the set of addresses under which node u can be<br />

reached. Viewed from a different perspective, if <strong>for</strong> a target address d ∈ D<br />

of a message, d ∈ coveru, node u will be eligible to receive and process the<br />

message. A node may be part of multiple trees and <strong>for</strong> every tree, the above<br />

predicate should yield a different part of the address space. For a specific tree<br />

t, we will there<strong>for</strong>e write cover (t)<br />

u .<br />

We require an operation <strong>for</strong> comb<strong>in</strong><strong>in</strong>g addresses, which we will denote as<br />

⊎. Two address covers D1,D2 ⊂ D comb<strong>in</strong>ed us<strong>in</strong>g this operation satisfy the

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