Bottleneck assignment problems under categorization

This paper considers two special cases of bottleneck grouped assignment problems when n jobs belong to m distinct categories (m < n). Solving these special problems through the available branch and bound algorithms will result in a heavy computational burden. Sequentially identifying nonopitmal variables, this paper provides more efficient methods for those cases. Propositions leading to the algorithms have been established. Numerical examples illustrate the respective algorithms.

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Demographic history of India and mtDNA-sequence diversity

The demographic history of India was examined by comparing mtDNA sequences obtained from members of three culturally divergent Indian subpopulations (endogamous caste groups). While an inferred tree revealed some clustering according to caste affiliation, there was no clear separation into three genetically distinct groups along caste lines. Comparison of pairwise nucleotide difference distributions, however, did indicate a difference in growth patterns between two of the castes. The Brahmin population appears to have undergone either a rapid expansion or steady growth. The low-ranking Mukri caste, however, may have either maintained a roughly constant population size or undergone multiple bottlenecks during that period. Comparison of the Indian sequences to those obtained from other populations, using a tree, revealed that the Indian sequences, along with ah other non-African samples, form a starlike cluster. This cluster may represent a major expansion, possibly originating in southern Asia, taking place at some point after modern humans initially left Africa.