Related papers: Communication Complexity of Cake Cutting
Suppose that Alice and Bob are given each an infinite string, and they want to decide whether their two strings are in a given relation. How much communication do they need? How can communication be even defined and measured for infinite…
We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare…
Envy-free cake-cutting protocols procedurally divide an infinitely divisible good among a set of agents so that no agent prefers another's allocation to their own. These protocols are highly complex and difficult to prove correct. Recently,…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
In the classic problem of fair cake-cutting, a single interval ("cake") has to be divided among n agents with different value measures, giving each agent a single sub-interval with a value of at least 1/n of the total. This paper studies a…
We discuss the communication complexity of establishing a shared reference frame, in particular examining the case of aligning spatial axes via the exchange of spin-1/2 particles. Unlike previous work we allow for multiple rounds of…
Deterministic and probabilistic communication protocols are introduced in which parties can exchange the values of polynomials (rather than bits in the usual setting). It is established a sharp lower bound $2n$ on the communication…
We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divisible "cake" with a necklace of discrete, indivisible…
We introduce a graphical framework for fair division in cake cutting, where comparisons between agents are limited by an underlying network structure. We generalize the classical fairness notions of envy-freeness and proportionality to this…
In this paper we study a max-min $k$-partition problem on a weighted graph, that could model a robust $k$-coalition formation. We settle the computational complexity of this problem as complete for class $\Sigma_2^P$. This hardness holds…
We study the problem of fairly allocating a divisible resource in the form of a graph, also known as graphical cake cutting. Unlike for the canonical interval cake, a connected envy-free allocation is not guaranteed to exist for a graphical…
This thesis is concerned with the design of distributed algorithms for solving optimization problems. We consider networks where each node has exclusive access to a cost function, and design algorithms that make all nodes cooperate to find…
This paper studies the one-way communication complexity of the subgroup membership problem, a classical problem closely related to basic questions in quantum computing. Here Alice receives, as input, a subgroup $H$ of a finite group $G$;…
The cake-cutting problem involves dividing a heterogeneous, divisible resource fairly between $n$ agents. Br\^{a}nzei et al. [6] introduced {\em generalised cut and choose} (GCC) protocols, a formal model for representing cake-cutting…
We consider the well-studied cake cutting problem in which the goal is to identify a fair allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer…
We study space-bounded communication complexity for unitary implementation in distributed quantum processors, where we restrict the number of qubits per processor to ensure practical relevance and technical non-triviality. We model…
We consider the classic cake-cutting problem of producing envy-free allocations, restricted to the case of four agents. The problem asks for a partition of the cake to four agents, so that every agent finds her piece at least as valuable as…
We present relation problems whose input size is $n$ such that they can be solved with no communication for entanglement-assisted quantum communication models, but require $\Omega(n)$ qubit communication for $2$-way quantum communication…
While exponential separations are known between quantum and randomized communication complexity for partial functions (Raz, STOC 1999), the best known separation between these measures for a total function is quadratic, witnessed by the…
In the classical cake cutting problem, a resource must be divided among agents with different utilities so that each agent believes they have received a fair share of the resource relative to the other agents. We introduce a variant of the…