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The sequential allocation protocol is a simple and popular mechanism to ...
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On the Complexity of Fair House Allocation
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Parametrized Complexity of Manipulating Sequential Allocation
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Precious Time: Understanding Social Stratification in the Knowledge Society Through Time Allocation
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Good Things Come to Those Who Swap Objects on Paths
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Bailouts in Financial Networks
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Thou Shalt Covet The Average Of Thy Neighbors' Cakes
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EnvyFree Allocations Respecting Social Networks
Finding an envyfree allocation of indivisible resources to agents is a central task in many multiagent systems. Often, nontrivial envyfree allocations do not exist, and, when they do, finding them can be computationally hard. Classical envyfreeness requires that every agent likes the resources allocated to it at least as much as the resources allocated to any other agent. In many situations this assumption can be relaxed since agents often do not even know each other. We enrich the envyfreeness concept by taking into account (directed) social networks of the agents. Thus, we require that every agent likes its own allocation at least as much as those of all its (out)neighbors. This leads to a "more local" concept of envyfreeness. We also consider a "strong" variant where every agent must like its own allocation more than those of all its (out)neighbors. We analyze the classical and the parameterized complexity of finding allocations that are complete and, at the same time, envyfree with respect to one of the variants of our new concept. To this end, we study different restrictions of the agents' preferences and of the social network structure. We identify cases that become easier (from Σ^p_2hard or NPhard to polynomialtime solvability) and cases that become harder (from polynomialtime solvability to NPhard) when comparing classical envyfreeness with our graph envyfreeness. Furthermore, we spot cases where graph envyfreeness is easier to decide than strong graph envyfreeness, and vice versa. On the route to one of our fixedparameter tractability results, we also establish a connection to a directed and colored variant of the classical SUBGRAPH ISOMORPHISM problem, thereby extending a known fixedparameter tractability result for the latter.
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