Logarithmic algorithms for fair division problems
Alexandr Grebennikov, Xenia Isaeva, Andrei V. Malyutin, Mikhail, Mikhailov, Oleg R. Musin
TL;DR
This paper investigates the query complexity of fair division problems, demonstrating that under certain conditions, a logarithmic number of queries suffices to find approximate solutions efficiently.
Contribution
It introduces logarithmic algorithms for fair division, showing they are effective under natural preference conditions.
Findings
Logarithmic query complexity for certain fair division classes
Efficient approximate solutions with minimal queries
Conditions under which logarithmic algorithms are optimal
Abstract
We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natural conditions on sets of preferences, a logarithmic number of queries with respect to accuracy is sufficient.
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Taxonomy
TopicsGame Theory and Voting Systems · Complexity and Algorithms in Graphs · Auction Theory and Applications