Communication complexity and convex optimization
Journal of Complexity
Test complexity of generic polynomials
Journal of Complexity
On the communication complexity of distributed algebraic computation
Journal of the ACM (JACM)
The communication complexity of computing differentiable functions in a multicomputer network
Theoretical Computer Science
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
Lower Bounds on Information Transfer in Distributed Computations
Journal of the ACM (JACM)
Truth revelation in approximately efficient combinatorial auctions
Proceedings of the 1st ACM conference on Electronic commerce
Sharing the cost of multicast transmissions
Journal of Computer and System Sciences - Special issue on Internet algorithms
Distributed algorithmic mechanism design: recent results and future directions
DIALM '02 Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications
Hardness Results for Multicast Cost Sharing
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Approximation techniques for utilitarian mechanism design
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A Communication Approach to the Superposition Problem
Fundamenta Informaticae - Hardest Boolean Functions and O.B. Lupanov
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In this paper, we introduce and develop the field of algebraic communication complexity, the theory dealing with the least number of messages to be exchanged between two players in order to compute the value of a polynomial or rational function depending on an input distributed between the two players. We define a general algebraic model, where the involved functions can be computed with the natural operations additions, multiplications and divisions and possibly with comparisons. We provide various lower bound techniques, mainly for fields of characteristic 0.We then apply this general theory to problems from distributed mechanism design, in particular to the multicast cost sharing problem, and study the number of messages that need to be exchanged to compute the outcome of the mechanism. This addresses a question raised by Feigenbaum, Papadimitriou, and Shenker [9].