| Summary: | 碩士 === 臺灣大學 === 資訊工程學研究所 === 98 === We consider the Capacitated Domination problem, which models a service requirement assignment scenario and is also a generalization of the well known Dominating Set problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service.
In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to different demand assignment models for this problem on general graphs, which also establishes the corresponding
approximating results to the well-known approximations of the traditional Dominating Set problem. Together with previously known results, this closes the problem of generally approximating the optimal solution.
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