
Good Things Come to Those Who Swap Objects on Paths
We study a simple exchange market, introduced by Gourvés, Lesca and Wilc...
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Object Reachability via Swaps under Strict and Weak Preferences
The Housing Market problem is a widely studied resource allocation probl...
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The Convergence of Iterative Delegations in Liquid Democracy in a Social Network
Liquid democracy is a collective decision making paradigm which lies bet...
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On the Enumeration of Bicriteria Temporal Paths
We discuss the complexity of path enumeration in weighted temporal graph...
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When Can Liquid Democracy Unveil the Truth?
In this paper, we investigate the socalled ODPproblem that has been fo...
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Parallel and Distributed Algorithms for the housing allocation Problem
We give parallel and distributed algorithms for the housing allocation p...
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Minimal Envy and Popular Matchings
We study expost fairness in the object allocation problem where objects...
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Object Allocation Over a Network of Objects: Mobile Agents with Strict Preferences
In recent work, Gourvès, Lesca, and Wilczynski propose a variant of the classic housing markets model where the matching between agents and objects evolves through Paretoimproving swaps between pairs of adjacent agents in a social network. To explore the swap dynamics of their model, they pose several basic questions concerning the set of reachable matchings. In their work and other followup works, these questions have been studied for various classes of graphs: stars, paths, generalized stars (i.e., trees where at most one vertex has degree greater than two), trees, and cliques. For generalized stars and trees, it remains open whether a Paretoefficient reachable matching can be found in polynomial time. In this paper, we pursue the same set of questions under a natural variant of their model. In our model, the social network is replaced by a network of objects, and a swap is allowed to take place between two agents if it is Paretoimproving and the associated objects are adjacent in the network. In those cases where the question of polynomialtime solvability versus NPhardness has been resolved for the social network model, we are able to show that the same result holds for the networkofobjects model. In addition, for our model, we present a polynomialtime algorithm for computing a Paretoefficient reachable matching in generalized star networks. Moreover, the object reachability algorithm that we present for path networks is significantly faster than the known polynomialtime algorithms for the same question in the social network model.
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