An efficient algorithm for maxdominance, with applications

Given a planar setS ofn points,maxdominance problems consist of computing, for everyp S, some function of the maxima of the subset ofS that is dominated byp. A number of geometric and graph-theoretic problems can be formulated as maxdominance problems, including the problem of computing a minimum independent dominating set in a permutation graph, the related problem of finding the shortest maximal increasing subsequence, the problem of enumerating restricted empty rectangles, and the related problem of computing the largest empty rectangle. We give an algorithm for optimally solving a class of maxdominance problems. A straightforward application of our algorithm yields improved time bounds for the above-mentioned problems. The techniques used in the algorithm are of independent interest, and include a linear-time tree computation that is likely to arise in other contexts.The research of this author was supported by the Office of Naval Research under Grants N00014-84-K-0502 and N00014-86-K-0689, and the National Science Foundation under Grant DCR-8451393, with matching funds from AT&T.This author's research was supported by the National Science Foundation under Grant DCR-8506361.