Object Reachability via Swaps along a Line

Huang, Sen; Xiao, Mingyu

doi:10.1609/aaai.v33i01.33012037

Cited by 10 publications

(11 citation statements)

References 13 publications

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“…The work of Gourvès et al left three of these problems open: Reachable Object on paths and Pareto Efficiency on generalized stars and trees. Subsequently, two sets of authors independently presented polynomialtime algorithms for Reachable Object on paths [4,11]. Both groups obtained an O(n 4 )-time algorithm by carefully studying the structure of swap dynamics on paths and then reducing the problem to 2-SAT.…”

Section: Introductionmentioning

confidence: 99%

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Object Allocation Over a Network of Objects: Mobile Agents with Strict Preferences

Li,

Plaxton,

Sinha

2021

Preprint

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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 Pareto-improving 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 follow-up 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 Pareto-efficient 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 Pareto-improving and the associated objects are adjacent in the network. In those cases where the question of polynomial-time solvability versus NP-hardness has been resolved for the social network model, we are able to show that the same result holds for the network-of-objects model. In addition, for our model, we present a polynomial-time algorithm for computing a Pareto-efficient reachable matching in generalized star networks. Moreover, the object reachability algorithm that we present for path networks is significantly faster than the known polynomial-time algorithms for the same question in the social network model.

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Section: Introductionmentioning

confidence: 99%

“…Related work. For the object-moving model, Huang and Xiao [11] study Reachable Object with weak preferences, i.e., where an agent can be indifferent between different objects. Bentert et al [4] establish NP-hardness for Reachable Object on cliques, and consider the case where the preference lists have bounded length.…”

Section: Introductionmentioning

confidence: 99%

Object Allocation Over a Network of Objects: Mobile Agents with Strict Preferences

Li,

Plaxton,

Sinha

2021

Preprint

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“…This also holds true for the special case of indivisible resources [Bouveret et al, 2016], which we concentrate on here. Moreover, we take into account the role of social networks built by agents, a growing line of research [Abebe et al, 2017, Bei et al, 2017, Bouveret et al, 2017, Bredereck et al, 2018, Chevaleyre et al, 2017, Beynier et al, 2019, Lange and Rothe, 2019, Huang and Xiao, 2019. We bring one further new aspect into this scenario, reflecting the increasing relevance of "sharing economies" [Belk et al, 2019, Schor andCansoy, 2019], where agents share resources in a peer-to-peer fashion.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, our goal is to improve an initial allocation through sharing resources between pairs of agents. Another line of research considers the improvement of allocations by exchanging items Chevaleyre et al [2007], Gourvès et al [2017], Huang and Xiao [2019]. There has been quite some work on bringing together resource allocation and social networks [Abebe et al, 2017, Bei et al, 2017, Bouveret et al, 2017, Bredereck et al, 2018, Chevaleyre et al, 2017, Beynier et al, 2019, Huang and Xiao, 2019.…”

Section: Introductionmentioning

confidence: 99%

On Improving Resource Allocations by Sharing

Bredereck¹,

Kaczmarczyk²,

Luo³

et al. 2021

Preprint

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Given an initial resource allocation, where some agents may envy others or where a different distribution of resources might lead to higher social welfare, our goal is to improve the allocation without reassigning resources. We consider a sharing concept allowing resources being shared with social network neighbors of the resource owners. To this end, we introduce a formal model that allows a central authority to compute an optimal sharing between neighbors based on an initial allocation. Advocating this point of view, we focus on the most basic scenario where a resource may be shared by two neighbors in a social network and each agent can participate in a bounded number of sharings. We present algorithms for optimizing utilitarian and egalitarian social welfare of allocations and for reducing the number of envious agents. In particular, we examine the computational complexity with respect to several natural parameters. Furthermore, we study cases with restricted social network structures and, among others, devise polynomial-time algorithms in path-and tree-like (hierarchical) social networks.

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“…Section 6 makes some concluding remarks. Partial results of this paper were presented on the thirty-third AAAI conference on artificial intelligence (AAAI 2019) and appeared as [22].…”

Section: Introductionmentioning

confidence: 99%

Object Reachability via Swaps under Strict and Weak Preferences

Huang

Xiao

2019

Preprint

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The Housing Market problem is a widely studied resource allocation problem. In this problem, each agent can only receive a single object and has preferences over all objects. Starting from an initial endowment, we want to reach a certain assignment via a sequence of rational trades. We first consider whether an object is reachable for a given agent under a social network, where a trade between two agents is allowed if they are neighbors in the network and no participant has a deficit from the trade. Assume that the preferences of the agents are strict (no tie among objects is allowed). This problem is polynomially solvable in a star-network and NP-complete in a tree-network. It is left as a challenging open problem whether the problem is polynomially solvable when the network is a path. We answer this open problem positively by giving a polynomial-time algorithm. Then we show that when the preferences of the agents are weak (ties among objects are allowed), the problem becomes NP-hard even when the network is a path. In addition, we consider the computational complexity of finding different optimal assignments for the problem under the network being a path or a star.

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Object Reachability via Swaps along a Line

Cited by 10 publications

References 13 publications

Object Allocation Over a Network of Objects: Mobile Agents with Strict Preferences

Object Allocation Over a Network of Objects: Mobile Agents with Strict Preferences

On Improving Resource Allocations by Sharing

Object Reachability via Swaps under Strict and Weak Preferences

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