Minimum Graph Covering with the Random Neural Network Model

Minimum graph (vertex) covering is an NP-hard problem arising in various areas (image processing, transportation models, plant layout, crew scheduling, etc.). We use the random network (RN) (Gelenbe 1989, 1990) to obtain its approximate solution; this model is very close to the “queueing networks with positive and negative customers” model we have also introduced (Gelenbe 1992). We compare the results obtained by our approach to the conventional greedy algorithm and to simulated annealing. The evaluation shows that the random network provides good results, at a computational cost less than that of simulated annealing but greater than that of the conventional greedy algorithm. The overall optimisation obtained is better with the RN approach, than with other published solution methods.