On total functions, existence theorems and computational complexity
Theoretical Computer Science
The fair and efficient division of the Winsor family silver
Management Science
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Sperner's lemma and robust machines
Computational Complexity
Fairness in Routing and Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Preference Elicitation and Query Learning
The Journal of Machine Learning Research
Cake cutting really is not a piece of cake
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fairness Measures for Resource Allocation
SIAM Journal on Computing
An approximation algorithm for max-min fair allocation of indivisible goods
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Matching algorithmic bounds for finding a Brouwer fixed point
Journal of the ACM (JACM)
Discrete Splittings of the Necklace
Mathematics of Operations Research
Minimizing the Worst Slowdown: Offline, Online
Operations Research
On the complexity of 2D discrete fixed point problem
Theoretical Computer Science
Some combinatorial Lemmas in topology
IBM Journal of Research and Development
Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders
Mathematics of Operations Research
Discrete Fixed Points: Models, Complexities, and Applications
Mathematics of Operations Research
On the black-box complexity of sperner's lemma
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
On the complexity of cake cutting
Discrete Optimization
Cake cutting: not just child's play
Communications of the ACM
Equilibrium analysis in cake cutting
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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We study the problem of finding an envy-free allocation of a cake to d + 1 players using d cuts. Two models are considered, namely, the oracle-function model and the polynomial-time function model. In the oracle-function model, we are interested in the number of times an algorithm has to query the players about their preferences to find an allocation with the envy less than ε. We derive a matching lower and upper bound of θ1/εd-1 for players with Lipschitz utilities and any d 1. In the polynomial-time function model, where the utility functions are given explicitly by polynomial-time algorithms, we show that the envy-free cake-cutting problem has the same complexity as finding a Brouwer's fixed point, or, more formally, it is PPAD-complete. On the flip side, for monotone utility functions, we propose a fully polynomial-time algorithm FPTAS to find an approximate envy-free allocation of a cake among three people using two cuts.