A Lemmas

Algorithm 5 finds such a network in poly (n, l) time. The sequence r (k) defined by (14) is a strictly increasing sequence. Appendix B.8. Lemma 6. F or any positive integer k, the sequence r (k) defined by (14) satisfies r ( k) 3 null 2 The number of closed connected subsets satisfying Definition 1 is a minimum. The interior and frontier (boundary) of a set X are denoted as Int X and Fr X, respectively. Proposition 1. F or any family of closed connected subsets satisfying Definition 1, all subsets are the Let S( k) be the collection of all permutations of the set [ k ].