Related papers: Hardness of Distributed Optimization
Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
We describe a simple deterministic $O( \varepsilon^{-1} \log \Delta)$ round distributed algorithm for $(2\alpha+1)(1 + \varepsilon)$ approximation of minimum weighted dominating set on graphs with arboricity at most $\alpha$. Here $\Delta$…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far…
By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(\Delta)$ rounds, where $\Delta$ is the maximum degree of the graph. We show that this is optimal: there is no distributed…
We study the minimum spanning tree (MST) problem in the massively parallel computation (MPC) model. Our focus is particularly on the *strictly sublinear* regime of MPC where the space per machine is $O(n^\delta)$. Here $n$ is the number of…
Over the past decade, a long line of research has investigated the distributed complexity landscape of locally checkable labeling (LCL) problems on bounded-degree graphs, culminating in an almost-complete classification on general graphs…
By far the most fruitful technique for showing lower bounds for the CONGEST model is reductions to two-party communication complexity. This technique has yielded nearly tight results for various fundamental problems such as distance…
We develop deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee. For $\epsilon>1/{\text{{poly}}}\log \Delta$ we obtain two algorithms with…
We study approximate distributed solutions to the weighted {\it all-pairs-shortest-paths} (APSP) problem in the CONGEST model. We obtain the following results. $1.$ A deterministic $(1+o(1))$-approximation to APSP in $\tilde{O}(n)$ rounds.…
We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent,…
We present a complete classification of the distributed computational complexity of local optimization problems in directed cycles for both the deterministic and the randomized LOCAL model. We show that for any local optimization problem…
$ \renewcommand{\tilde}{\widetilde} $We present an $\tilde{O}(\log^2 n)$ round deterministic distributed algorithm for the maximal independent set problem. By known reductions, this round complexity extends also to maximal matching,…
We revisit classical connectivity problems in the CONGEST model of distributed computing. By using techniques from fault tolerant network design, we show improved constructions, some of which are even "local" (i.e., with $\widetilde{O}(1)$…
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 consider a class of convex optimization problems over the simplex of probability measures. Our framework comprises optimal experimental design (OED) problems, in which the measure over the design space indicates which experiments are…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…