The complexity of the Weight Problem for permutation groups Peter J Cameron 1 School of Mathematical Sciences Queen Mary, University of London London, E1 4NS, UK Taoyang Wu 2 Department of Computer Science and School of Mathematical Sciences Queen Mary, University of London London, E1 4NS, UK Abstract Given a metric d on a permutation group G, the corresponding weight problem is to decide whether there exists an element g ∈ G such that d(g,e)= k for some k ∈ N. In this paper we show that this problem is NP-complete for many well known metrics. Keywords: Weight Problem, Metrics, Permutation Group, NP-complete 1 Email: P.J.Cameron@qmul.ac.uk 2 Email: Taoyang.Wu@dcs.qmul.ac.uk