A general construction for deletion/insertion correcting codes is proposed by concatenating codes derived from a heuristic maximal independent set algorithm on an appropriately defined graph. Our heuristic algorithm is polynomial with respect to the number of nodes in the graph. This methodology may be used for construction of any length n, s-deletion code. Our experimental results show that cardinalities of our codebooks exceed sizes of all previously known constructions. In fact, they are comparable to Levenshteins lower bound.