Related papers: Communication Complexity of Cake Cutting
The topology-aware Massively Parallel Computation (MPC) model is proposed and studied recently, which enhances the classical MPC model by the awareness of network topology. The work of Hu et al. on topology-aware MPC model considers only…
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…
We consider the learning and communication complexity of subsequence containment. In the learning problem, we seek to learn a classifier that positively labels a binary string $x$ if it contains a fixed binary string $y$ as a subsequence.…
We initiate the theory of communication complexity of individual inputs held by the agents, rather than worst-case or average-case. We consider total, partial, and partially correct protocols, one-way versus two-way, with and without help…
Set disjointness is a central problem in communication complexity. Here Alice and Bob each receive a subset of an n-element universe, and they need to decide whether their inputs intersect or not. The communication complexity of this…
This work addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research, which can be viewed as demonstrating qualitative advantage of quantum communication in the three…
This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game…
In this work, we introduce an online model for communication complexity. Analogous to how online algorithms receive their input piece-by-piece, our model presents one of the players, Bob, his input piece-by-piece, and has the players Alice…
We study the fair division problem on divisible heterogeneous resources (the cake cutting problem) with strategic agents, where each agent can manipulate his/her private valuation in order to receive a better allocation. A…
We consider the classic cake cutting problem in the Robertson-Webb model, with the objective of proportional fairness. We show that any randomized algorithm must use $\Omega(n \log n)$ queries.
We study the one-way two-party communication complexity of Maximum Matching in the semi-robust setting where the edges of a maximum matching are randomly partitioned between Alice and Bob, but all remaining edges of the input graph are…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g., a cake, between n players. Our framework follows the same idea than the ''Full independence model'' used in the study of…
Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [Buh98]…
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It…
Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function…
We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this…
Heterogeneity within data distribution poses a challenge in many modern federated learning tasks. We formalize it as an optimization problem involving a computationally heavy composite under data similarity. By employing different sets of…
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating the process of preparation, transmission through the channel, and subsequent measurement of a quantum…
We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing,…