A Memory-Storable Quantum-Inspired Evolutionary Algorithm for Network Coding Resource Minimization

Network coding technology is a new communication paradigm that is superior to traditional routing in many aspects, especially in terms of the ability of increasing multicast throughput (Ahlswede et al., 2000; Li et al., 2003). Traditional routing adopts store-andforward data forwarding scheme at every intermediate node that simply replicates and forwards the incoming data to downstream nodes. However, the maximum throughput of a multicast scenario could not be often achieved under such a scheme (Ahlswede et al., 2000; Li et al., 2003). With code-and-forward data forwarding scheme at network layer, network coding allows arbitrary intermediate node to combine (or code) the data received from different incoming links and output the coded information if necessary, being able to obtain a multicast throughput that is maximized according to the MAX-FLOW MIN-CUT theorem (Li et al., 2003). Fig. 1 shows why network coding performs better than traditional routing in terms of the maximum multicast throughput they achieve. Fig.1(a) shows a network with source s and sinks y, z. Each direct link has a capacity of 1 bit per time unit. Source s expects to send two bits, a and b, to y and z. According to the MAX-FLOW MIN-CUT theorem, the min cut Cmin between s and {y, z} is 2 bits per time unit, which means the maximum multicast throughput from s to y and z should be 2 bits per time unit. However, if traditional routing is adopted, the multicast throughput is 1.5 bits information per time unit since link wåx could only forward 1 bit, a or b, to x, and thus y and z can not simultaneously receive two bits, a and b, as indicated in Fig.1(b). In Fig.1(c), if the intermediate node w is allowed to combine the 2 bits, a and b, it receives from t and u respectively to 1 bit a⊕b (here, symbol ⊕ is ExclusiveOR operation) and output a⊕b to x, y and z are both able to obtain {a, a⊕b} and {b, a⊕b}, which means two bits information is available at both y and z. Meanwhile, y and z can use {a, a⊕b} and {b, a⊕b} to decode b and a by calculate a⊕(a⊕b) and b⊕(a⊕b) respectively. To the best of our knowledge, most of the network-coding-related research works suppose that coding operation should be implemented at all coding-possible intermediate nodes. However, to achieve a desired throughput, coding operation may only be necessarily performed at a subset of those nodes (Kim et al., 2006; 2007a; 2007b). In Fig.2, there are two network coding schemes that could both achieve the maximum multicast throughput. Network coding scheme A adopts all coding-possible nodes, m and n, as shown in Fig.2(a).