# Distributed Reliable and Efficient Transmission Task Assignment for WSNs
## 5 Reliable and Efficient Task Allocation Algorithm for WSNs
### Distributed Task Assignment
#### 5.2.2 Distributed Reliable and Efficient Task Allocation in Planar Topology


\begin{tabular}{l l} \(RT(S,Ps)\) & Routing topology of the network \\ \(M(t)\) & Task set to be assigned at time \(t\) \\ \(\varphi(m_{i})\) & Mapped function of \(m_{i}\) \\ \(Eng(\varphi(m_{i}))\) & Energy consumption of the task \(m_{i}\) \\ \(RT_{b}(S,Ps)\) & Physical topology of the backbone network \\ \(TG_{b}(S,Ps)\) & Routing topology of the backbone network \\ \(TG_{c}(S,Ps)\) & The physical topology of the intra-cluster \\ \(RT_{c}(S,Ps)\) & Routing topology of the intra-cluster \\ \(TG_{b^{\prime}}(V,E)\) & Physical topology after backbone network update \\ \(RT_{b^{\prime}}(S,Ps)\) & Routing topology after backbone network update \\ \(TG_{c^{\prime}}(V,E)\) & Physical topology of the intra-cluster after update \\ \(RT_{c^{\prime}}(S,Ps)\) & Routing topology of the intra-cluster after update \\ \(TG_{j}(V,E)\) & Local physical topology of the \(j\)-th sink in a multi-sink topology \\ \(RT_{j}(S,Ps)\) & Local routing topology of the \(j\)-th sink in a multi-sink topology \\ \(sink_{j}\) & The closest sink to the task \(m_{i}\) \\ \(sink_{jn}\) & Sink adjacent to \(sink_{j}\) \\ \(sink_{k}\) & Sink involving topology changes \\ \(viewID\) & The version ID of the global view \\ \(PathSet_{m_{i}}\) & Path set of the source node to the sink in the coverage area of the task \(m_{i}\) \\ \(PathSet_{m_{i}}\) & Path set after deleting the paths with link conflict in \(PathSet_{m_{i}}\) \\ \(Paths_{i}\) & Transmission path of each source node \(s_{i}\) to sink in \(PathSet_{m_{i}}\), \\ \(R_{s_{i}}\) & Reliability of \(Paths_{i}\) \\ \(E_{s_{i}}\) & Energy consumption of \(Paths_{i}\) \\ \(path_{R_{s}}\) & Path to meet the target reliability \(R_{s}\) \\ \(R_{CH}\) & Target reliability of cluster head to sink after reliability allocation \\ \(R_{CH^{\prime}}\) & Updated \(R_{CH}\) \\ \(R_{CM}\) & Target reliability of cluster head after reliability allocation \\ \(sink^{\prime\prime\prime}_{k}\) & Sink respond to update request of \(sink_{k}\) \\ \(sink^{\prime\prime\prime}_{k}.RT_{j}(S,Ps)\) & Routing topology of the j-th sink in \(sink^{\prime\prime\prime}_{k}\) \\ \(sink^{\prime\prime\prime}_{k}.TG_{j}(V,E)\) & Physical topology of the j-th sink in \(sink^{\prime\prime\prime}_{k}\) \\ \(sink_{k}.record\) & Update operation record of \(sink_{k}\) \\ \(sink^{\prime\prime\prime}_{k}.log\) & Log of sink which respond to update \\ \(Sw\), \(S_{R}\) & Quorum set of writing and reading \\ \(P_{overlap}\) & Overlapping probability of \(S_{W}\) and \(S_{R}\) \\ \(CM\) & Communication load \\ \(Num_{cp}\) & Number of packets in the allocation policy by multicast, \\ \(Num_{gp}\) & Communication load for transmitting one global view \\ \(WM\), \(RW\) & Writing load, reading load \\ \(V



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