Related papers: New Bounds for the Garden-Hose Model
We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…
A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded…
We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
The main difficulty when modelling gene networks is the identification of the parameters that govern their dynamics. It is particularly difficult for models in which time is continuous: parameters have real values which cannot be…
We prove the first nontrivial worst-case lower bounds for two closely related problems. First, $\Omega(n^{3/2})$ degree-1 reductions, series-parallel reductions, and $\Delta$Y transformations are required in the worst case to reduce an…
In this paper we develop a new technique for proving lower bounds on the update time and query time of dynamic data structures in the cell probe model. With this technique, we prove the highest lower bound to date for any explicit problem,…
In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…
We develop a new technique for computing higher limits of functors over filtered posets by constructing explicit fibrant replacements within a suitable model category structure. We apply this procedure to develop two systematic vanishing…
We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot…
The $CONGEST$ model for distributed network computing is well suited for analyzing the impact of limiting the throughput of a network on its capacity to solve tasks efficiently. For many "global" problems there exists a lower bound of…
Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
Given an $n$-point metric space $(X,d_X)$, a tree cover $\mathcal{T}$ is a set of $|\mathcal{T}|=k$ trees on $X$ such that every pair of vertices in $X$ has a low-distortion path in one of the trees in $\mathcal{T}$. Tree covers have been…
We explore multi-round quantum memoryless communication protocols. These are restricted version of multi-round quantum communication protocols. The "memoryless" term means that players forget history from previous rounds, and their behavior…
We establish enhanced bounds on Cheeger-Gromov rho-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by…
In this paper we initiate a study of distributed deterministic broadcasting in ad-hoc wireless networks with uniform transmission powers under the SINR model. We design algorithms in two settings: with and without local knowledge about…
In distributed stochastic optimization, where parallel and asynchronous methods are employed, we establish optimal time complexities under virtually any computation behavior of workers/devices/CPUs/GPUs, capturing potential disconnections…
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…
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…
This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities…