Imagining Evil: George MacDonald\u27s The Wise Woman: A Parable (1875)

Discusses a neglected and uncharacteristic children\u27s story, The Wise Woman, by the Victorian Scottish novelist and fantasy writer George MacDonald, setting it in the context of MacDonald\u27s own development and of other Victorian children\u27s moral fantasy, concluding that The Wise Woman is not simply a story of the attempted correction of two children, but a vision of good and evil in the mind and in God’s creation.... In its moral and spiritual complexity, and its picture of divine grace all about us if we will open our hearts, The Wise Woman has a profundity and a lucidity that gives it a place among MacDonald’s best creations

Popular Matchings in the Weighted Capacitated House Allocation Problem

We consider the problem of finding a popular matching in the Weighted Capacitated House Allocation problem (WCHA). An instance of WCHA involves a set of agents and a set of houses. Each agent has a positive weight indicating his priority, and a preference list in which a subset of houses are ranked in strict order. Each house has a capacity that indicates the maximum number of agents who could be matched to it. A matching M of agents to houses is popular if there is no other matching M′ such that the total weight of the agents who prefer their allocation in M′ to that in M exceeds the total weight of the agents who prefer their allocation in M to that in M′ . Here, we give an O( √ Cn1 + m) algorithm to determine if an instance of WCHA admits a popular matching, and if so, to find a largest such matching, where C is the total capacity of the houses, n1 is the number of agents, and m is the total length of the agents’ preference lists