Ayumi Igarashi, Naoyuki Kamiyama, Warut Suksompong, Sheung Man Yuen
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Reachability of Fair Allocations via Sequential Exchanges
In the allocation of indivisible goods, a prominent fairness notion is envy-freeness up to one good (EF1). We initiate the study of reachability problems in fair division by investigating the problem of whether one EF1 allocation can be reached from another EF1 allocation via a sequence of exchanges such that every intermediate allocation is also EF1. We show that two EF1 allocations may not be reachable from each other even in the case of two agents, and deciding their reachability is PSPACE-complete in general. On the other hand, we prove that reachability is guaranteed for two agents with identical or binary utilities as well as for any number of agents with identical binary utilities. We also examine the complexity of deciding whether there is an EF1 exchange sequence that is optimal in the number of exchanges required.
期刊介绍：
Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential.
Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming.
In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.
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