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The paper took different regions and regional industries as initial water right allocation objects in the basin; the compound system for basin initial water right allocation was given; the connotation and objective of the compound system was analyzed; and the bi-level optimization model of the compound system optimization was established to allocate water right of different regions and regional industries, and eliminate the water conflict and contradiction among regions, embody the fairness and efficiency of different regions' water right, prevent different industries from the vicious water right competition, optimize comprehensive benefit of society-economy-ecology in the basin. Meanwhile, according to the interactive decision-making theory, the model algorithm was put forward. The case analysis verified the effectiveness of the model. [ABSTRACT FROM AUTHOR]

In the actual process of locating facility, the decision-maker always faces the following constraints: they must determine where to locate the initial facility (or facilities) when the number of edges to be served is uncertain, and, the constructed facilities can not be removed when the new facility is built. The existed models and algorithms are always pointed to a static facility location process, but here we need a dynamic facility location model with above constraints. Considered the online vertex covering problem in this paper, we present a structural lower bound which does not need any complexity assumption, and prove that the analysis is tight by giving a competitive algorithm as well as competitive ratio proof for a restricted version of the online vertex covering problem, and we also obtain that this algorithm is optimal if we are permitted to use non-polynomial time. [ABSTRACT FROM AUTHOR]