A Novel Method to Solve the Maximum Weight Clique Problem for Instantly Decodable Network Coding

Minimizing the decoding delay, the completion time, or the delivery time of instantly decodable network coding (IDNC) can all be approximated to a maximum weight clique (MWC) problem, which is well known to be NP hard. Due to its good tradeoff between performance and computational complexity, a heuristic approach named as maximum weight vertex (MWV) search is widely employed to select MWC for IDNC. However, in MWV, when there are few coding connection edges among the adjacent vertices of a vertex, its modified vertex weight cannot well reflect the weight of the MWC containing the vertex, which leads to incorrect selection of MWC. This paper proposes a new method to calculate the modified weight of a vertex by summing the weights of the vertices in the approximate maximum weight path (A-MWP) generated by this vertex. Since the vertices in an A-MWP can form a maximal clique, the proposed modified vertex weight may well indicate the weight of the MWC containing the vertex. The proposed algorithm has the same computational complexity as the MWV algorithm. Simulation results show that when employing any of the three performance metrics of IDNC, our proposed algorithm can achieve better system performance than the MWV algorithm.