The complexity of the weight problem for permutation and matrix groups

Given a metric d on a permutation group G, the corresponding weight problem is to decide whether there exists an element G such that d(, e) = k, for some given value k. Here we show that this problem is NP-complete for many well-known metrics. An analogous problem in matrix groups, eigenvalue-free problem, and two related problems in permutation groups, the maximum and minimum weight problems, are also investigated in this paper. Key words: Weight Problem, Metrics, Permutation Group, NP-complete

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Peter J. Cameron, Taoyang Wu
• Keywords: Corresponding Weight Problem, DM 2010, Permutation Group, Weight Problem