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We consider the point-to-point message passing model of communication in which there are $k$ processors with individual private inputs, each $n$-bit long. Each processor is located at the node of an underlying undirected graph and has access to private random coins. An edge of the graph is a private channel of communication between its endpoints. The processors have to compute a given function of all their inputs by communicating along these channels. While this model has been widely used in distributed computing, strong lower bounds on the amount of communication needed to compute simple functions have just begun to appear. In this work, we prove a tight lower bound of $Omega(kn)$ on the communication needed for computing the Tribes function, when the underlying graph is a star of $k+1$ nodes that has $k$ leaves with inputs and a center with no input. Lower bound on this topology easily implies comparable bounds for others. Our lower bounds are obtained by building upon the recent information theoretic techniques of Braverman et.al (FOCS13) and combining it with the earlier work of Jayram, Kumar and Sivakumar (STOC03). This approach yields information complexity bounds that is of independent interest.
We study the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, proving a number of tight lower bounds. Specifically, for a matrix which is distributed among a number of players, we con
We show that disjointness requires randomized communication Omega(n^{1/(k+1)}/2^{2^k}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound for k >= 3 was log(n)/(k-1). Our results give a separation between
We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is PSPACE-complete; and (3) cooperati
Graph neural networks (GNNs) are a powerful inductive bias for modelling algorithmic reasoning procedures and data structures. Their prowess was mainly demonstrated on tasks featuring Markovian dynamics, where querying any associated data structure d
In a multiparty message-passing model of communication, there are $k$ players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in distributed c