Complexity of Efficient and Envy-Free Resource Allocation: Few Agents, Resources, or Utility Levels
نویسندگان
چکیده
We study the problem of finding a Pareto-efficient and envy-free allocation of a set of indivisible resources to a set of agents with monotonic preferences, either dichotomous or additive. Motivated by results of Bouveret and Lang [JAIR 2008], we provide a refined computational complexity analysis by studying the influence of three natural parameters: the number n of agents, the number m of resources, and the number z of different numbers occurring in utility-based preferences of the agents. On the negative side, we show that small values for n and z alone do not significantly lower the computational complexity in most cases. On the positive side, devising fixed-parameter algorithms we show that all considered problems are tractable in case of small m. Furthermore, we develop a fixed-parameter algorithm indicating that the problem with additive preferences becomes computationally tractable in case of small n and small z.
منابع مشابه
Three New Complexity Results for Resource Allocation Problems
We prove the following results for task allocation of indivisible resources: • The problem of finding a leximin-maximal resource allocation is in P if the agents have max-utility functions and atomic demands. • Deciding whether a resource allocation is Pareto-optimal is coNP-complete for agents with (1-)additive utility functions. • Deciding whether there exists a Pareto-optimal and envy-free r...
متن کاملNegotiating efficient envy-free divisions
Division of a resource among multiple agents is a frequent problem in multiagent systems and fair, efficient, and decentralized allocation procedures are highly valued. A division of a resource or good is envy-free when every agent believes that its share is not less than anyone else’s share by its own estimate. As envy-free procedures are not efficient (in the sense of Pareto optimality) we ha...
متن کاملEnvy-ratio and average-nash social welfare optimization in multiagent resource allocation
The resource allocation problem deals with distributing a number of indivisible, nonshareable resources among a set of agents so as to optimizing social welfare. Assuming all agents to have additive utility functions and focusing on two particular measures of social welfare, envy-ratio and average-Nash product, we investigate the two resulting optimization problems. We give the first hardness o...
متن کاملA New Fairness Index and Novel Approach for QoS-Aware Resource Allocation in LTE Networks Based on Utility Functions
Resource allocation techniques have recently appeared as a widely recognized feature in LTE networks. Most of existing approaches in resource allocation focus on maximizing network’s utility functions. The great potential of utility function in improving resource allocation and enhancing fairness and mean opinion score (MOS) indexes has attracted large efforts over the last few years. In this p...
متن کاملMore than Envy-Free
There have been several interesting results in the literature on dividing up goods between self-interested parties such that the allocation is envy-free (Brams Taylor 1996). An allocation is deemed envy-free when every party (agent) believes that its share is not less than anyone else’s share. These procedures, however, are not efficient (in the sense of pareto optimality) general. Envy-free pr...
متن کامل