Related papers: New Bounds for the Garden-Hose Model

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…

In this paper we provide new bounds on classical and quantum distributional communication complexity in the two-party, one-way model of communication. In the classical model, our bound extends the well known upper bound of Kremer, Nisan and…

In this paper, we study the dynamics of contagious spreading processes taking place in complex contact networks. We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible-infected-susceptible…

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…

The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…

We consider the class of functions whose value depends only on the intersection of the input X_1,X_2, ..., X_t; that is, for each F in this class there is an f_F: 2^{[n]} \to {0,1}, such that F(X_1,X_2, ..., X_t) = f_F(X_1 \cap X_2 \cap ...…

The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…

In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…

We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it…

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

Many recent algorithms for approximate model counting are based on a reduction to combinatorial searches over random subsets of the space defined by parity or XOR constraints. Long parity constraints (involving many variables) provide…

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…

Recently, Balliu, Brandt, and Olivetti [FOCS '20] showed the first $\omega(\log^* n)$ lower bound for the maximal independent set (MIS) problem in trees. In this work we prove lower bounds for a much more relaxed family of distributed…

Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting $n$ processes is dynamic (e.g., due to mobility or failures)…

The $\hybrid$ model was recently introduced by Augustine et al. \cite{DBLP:conf/soda/AugustineHKSS20} in order to characterize from an algorithmic standpoint the capabilities of networks which combine multiple communication modes.…

Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…

We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…

We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…

We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…

We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…