The modularity is the best known and widely used quality function for community detection in graphs. We investigate approximability of maximization problem some related problems. first design a polynomial-time 0.4209-additive approximation algorithm problem, which improves current additive error 0.4672. Our theoretical analysis also demonstrates that proposed obtains nearly-optimal solution any...

Many of the optimization problems we would like to solve are NP hard There are several ways of coping with this apparent hardness For most problems there are straightforward exhaustive search algorithms and one could try to speed up such an algorithm Techniques which can be used include divide and conquer or the re ned branch and bound which allows to eliminate part of the search tree by comput...