Recently, the problem of allocating one resource per agent with initial endowments () has seen a renewed interest: indeed, while in the general domain Top Trading Cycle is known to be the only procedure guaranteeing Pareto-optimality, individual rationality, and strategy proofness, the situation differs in single-peaked domains. Bade (2019) presented the Crawler, an alternative procedure enjoying the same properties (with the additional advantage of being implementable in obviously dominant strategies); while (2015) showed that allowing mutually beneficial swap-deals among the agents was already enough to guarantee Pareto-optimality. In this paper we significantly deepen our understanding of this decentralized procedures: we show in particular that the single-peaked domains happen to be maximal'' if one wishes to guarantee this convergence property. Interestingly, we also observe that the set of allocations reachable by swap-deals always contains the outcome of the Crawler. To further investigate how these different mechanisms compare, we pay special attention to the average and minimum rank of the resource obtained by the agents in the outcome allocation. We provide theoretical bounds on the loss potentially induced by these procedures with respect to these criteria, and complement these results with an extensive experimental study which shows how different variants of swap dynamics behave. In fact, even the simplest dynamics exhibit very good results, and it is possible to further guide the process towards our objectives, if one is ready to sacrifice a bit in terms of decentralization. On our way, we also show that a simple variant of the Crawler allows to check efficiently that an allocation is Pareto-optimal in single-peaked domains.
Most of the procedures we talked about, among which the TTC algorithm, are centralized procedures which rely on a benevolent entity to proceed. Of particular interest for us are the decentralized procedures. A growing literature exists on such procedures. @cite_21 and @cite_14 respectively introduced the and the , two semi-decentralized procedures where the agents announce their preferred resources to a referee. These procedures return envy-free and balanced allocations when there are two agents. Another semi-decentralized procedure is the in which agents come in turn to pick one of the remaining resource .
@cite_14 @cite_21
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We consider the problem of reallocating indivisible objects amongst a set of agents when the preference ordering of each agent may contain indifferences. The same model, but with strict preferences, goes back to the seminal work of Shapley and Scarf in 1974. When preferences are strict, we now know that the Top-Trading Cycles (TTC) mechanism invented by Gale is Pareto efficient, strategy-proof, and finds a core allocation, and that it is the only mechanism satisfying these properties. In the extensive literature on this problem since then, the TTC mechanism has been characterized in multiple ways, establishing its central role within the class of all allocation mechanisms. The question motivating our work is the extent to which these results can be generalized to the setting with indifferences. Our main contribution is a general framework to design strategyproof mechanisms that find a Pareto optimal allocation in the weak-core. Along the way, we establish a sufficient condition for a mechanism (within a broad class of mechanisms) to be strategyproof and use this condition to design fast algorithms for finding a "good" reallocation. Our results generalize and unify two (different) mechanisms for the reallocation problem derived, independently of each other, by Manjunath and Jaramillo, and Alcalde-Unzu and Molis. Matching a set of agents to a set of objects has many real applications. One well-studied framework is that of priority-based matching, in which each object is assumed to have a priority order over the agents. The Deferred Acceptance (DA) and Top-Trading-Cycle (TTC) mechanisms are the best-known strategy-proof mechanisms. However, in highly anonymous environments, the set of agents is not known a priori, and it is more natural for objects to instead have priorities over characteristics (e.g., the student's GPA or home address). In this paper, we extend the model so that each agent reports not only its preferences over objects, but also its characteristic. We derive results for various notions of strategy-proofness and false-name-proofness, corresponding to whether agents can only report weaker characteristics or also incomparable or stronger ones, and whether agents can only claim objects allocated to their true accounts or also those allocated to their fake accounts. Among other results, we show that DA and TTC satisfy a weak version of false-name-proofness. Furthermore, DA also satisfies a strong version of false-name-proofness, while TTC fails to satisfy it without an acyclicity assumption on priorities. This paper proposes a dynamic semi-centralized resource partitioning algorithm to mitigate the problem of co-tier interference in dense femtocell deployments. This algorithm incorporates graph-colouring and network utility concepts to address inter-cell interference in femtocell networks. The aforementioned scheme acts as a multi-cell coordination mechanism on top of intra-cell scheduling by applying a low complexity graph-based algorithm. The objective of the coordination mechanism is the efficient management of resource conflicts due to interference in a multi-cell environment consisting of femtocells. This coordination mechanism defines a novel category of graph-based ICIC algorithms that uses bipartite graph colouring to avoid resource conflicts by randomizing them in time domain. In this paper, a novel decentralized task allocation algorithm based on the Hungarian approach is proposed. The proposed algorithm guarantees an optimal solution as long as the agent network is connected, i.e., the second smallest eigenvalue of the Laplacian matrix of the agent graph is greater than zero. In order to show the motivation of the proposed algorithm, the original centralized auction and Hungarian algorithms are compared in terms of the converging speed versus the number of agents. The result shows the superiority of the Hungarian algorithm in scalability over the auction algorithm. Then, the performance of the proposed decentralized Hungarian-Based algorithm (DHBA) is compared with the consensus-based auction algorithm (CBAA) under different situations, including different number of agents and different network topologies. The simulation results show that DHBA outperforms CBAA in all cases on the basis of the converging speed, the optimality of assignments, and the computational time.