## 5 Comparison of Different Topologies
### Topology Comparison Based on Energy Efficiency  
Energy efficiency is the most important constraint and performance metric for WSNs due to the limited energy resources of the sensor nodes and their operations in unattended and inaccessible environments where replacement of energy resources might be impossible. Therefore, while traditional networks aim at achieving high quality-of-service provisions, WSNs focus primarily on energy awareness in every aspect of hardware and software design and operations to prolong the useful lifetime of each sensor node and, more importantly, of the entire WSN [75]. Communication is the most energy intensive activity performed by the sensor nodes, and hence the WSN topology and communication protocols can play a significant role in the energy efficiency and lifetime of the WSN. Figure 6 depicts the communication patterns of basic cluster, chain and tree topologies. The energy required for communication scales with distance between two nodes (\(d\)) from \(d^{2}\) to \(d^{4}\). Since the radio signal attenuation scales with distance in a greater-than-linear fashion, the multi-hop communication in chain topology consumes less power than the single-hop long distance radio communication in cluster topology [76]. In chain-based topologies, chains are usually formed considering the minimum distance from a node in the chain to its successor. On the other hand, while configuring clusters, distance has never been used as a selection criterion. Simulation results show that summation of d2 values is the minimum for a chain-oriented topology compared with cluster-based or tree-based topologies. As the total energy consumption is directly proportional to the \(d^{2}\) / \(d^{4}\), total energy consumption for chain-based topology is always lower than other topologies. For example, PEGASIS spends only 70% of total energy spent by LEACH for 300 rounds of data collection [71]. Energy consumption of the sensor nodes of a WSN should be evenly distributed. If some node spends too much energy to perform a task, by repetition of that task, those nodes would lose their energy rapidly and die soon. It is apparent from Figure 6 that, in cluster and tree topologies, CHs (cluster topology) and parents nodes (tree topology) handle more traffic than the leader node(s) of chain topology. As a result, those nodes in cluster and tree topologies deplete their energy faster than other nodes, and thereby disconnecting the base station from the whole WSN, which might still have adequate resources and infrastructure. This is the well-known self-induced black hole effect. Simulations shows that nodes closest to the base station are the ones to die out first for flat mesh routing, whereas nodes farthest from the base station are the ones to die out first for direct transmission [77]. In-network processing, which is primarily based on the motivation that typically computation is more energy-efficient than communication, is one of the key mechanisms with the potential to considerably improve the energy efficiency of WSNs. Simulations have shown that it typically requires around 100 to 1000 times more energy to transmit a bit than to execute an instruction [78]. Possibilities for in-network processing in WSN include aggregation and compression, which exploit spatial and temporal correlation in the sensed data, for performing local compression to reduce global communication to base station by reducing the overhead of packet headers, by compressing the payload, and by reducing the probability of packet collisions. For example, the predominant communication in WSN is converge-cast, _i.e._, collection of sensed data from multiple sensors at the base station: a kind of reverse multicast. In addition, coverage-cast aligns closely with the need and capacity of WSN to perform in-network processing. In a flat topology, routing paths are not fixed a priori, and hence the opportunity for the in-network processing is very much limited.