Improvement of Extended Least Difference Greedy Clique-Cover Algorithm for Index Coding

We modify the heuristic algorithm proposed by Kwak, et al., called the extended least difference greedy (ELDG) algorithm, to make it more efficient. The column-merging heuristic algorithm, which is one of the essential parts in the ELDG algorithm, is found numerically not to be efficient for reducing the index codelength; besides, the result of the column-merging heuristic algorithm can be even longer than that of the original LDG algorithm. We detect when the column-merging heuristic algorithm give worse result than the result of the original LDG algorithm. Modified slightly, the proposed column-merging heuristic algorithm becomes efficient for reducing codelength. Additionally, we add the cycle-of-p-nodes detection algorithm, which is the generalized version of the cycle-of-three-node detection algorithm in the ELDG algorithm. It is numerically shown that roughly 20% of the index codelength reduction is achieved by the proposed ELDG algorithm compared to the LDG algorithm, while the conventional ELDG algorithm shows 10% of reduction rate compared to the LDG algorithm.