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

Abstract

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.