相关论文: Rounding Dynamic Matchings Against an Adaptive Adv…
A dynamic algorithm against an adaptive adversary is required to be correct when the adversary chooses the next update after seeing the previous outputs of the algorithm. We obtain faster dynamic algorithms against an adaptive adversary and…
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first…
Designing dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms. While a few such algorithms are known for spanning trees, matchings, and single-source shortest paths, very little…
In the fully dynamic maximal matching problem, the goal is to maintain a maximal matching in a graph undergoing an online sequence of edge insertions and deletions. The problem has been studied extensively in the oblivious-adversary…
We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms. Applying this reduction to the recent fractional matching algorithm of…
We study dynamic $(1-\epsilon)$-approximate rounding of fractional matchings -- a key ingredient in numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is a surprisingly simple deterministic rounding…
We provide an algorithm that maintains, against an adaptive adversary, a $(1-\varepsilon)$-approximate maximum matching in $n$-node $m$-edge general (not necessarily bipartite) undirected graph undergoing edge deletions with high…
We study dynamic algorithms robust to adaptive input generated from sources with bounded capabilities, such as sparsity or limited interaction. For example, we consider robust linear algebraic algorithms when the updates to the input are…
The rapidly changing landscapes of modern optimization problems require algorithms that can be adapted in real-time. This paper introduces an Adaptive Metaheuristic Framework (AMF) designed for dynamic environments. It is capable of…
We introduce new techniques for proving lower bounds on the running time of randomized algorithms for asynchronous agreement against powerful adversaries. In particular, we define a \emph{strongly adaptive adversary} that is computationally…
We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…
We study the dynamic correlation clustering problem with $\textit{adaptive}$ edge label flips. In correlation clustering, we are given a $n$-vertex complete graph whose edges are labeled either $(+)$ or $(-)$, and the goal is to minimize…
In this paper, we present a construction of a `matching sparsifier', that is, a sparse subgraph of the given graph that preserves large matchings approximately and is robust to modifications of the graph. We use this matching sparsifier to…
The vulnerability of deep neural network models to adversarial example attacks is a practical challenge in many artificial intelligence applications. A recent line of work shows that the use of randomization in adversarial training is the…
We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update. Our main result is a data structure that maintains a $(1+\epsilon)$…
In this note, we revisit the rounding algorithm of Wajc. Wajc gave a fully-adaptive randomized algorithm that rounds a dynamic fractional matching in an unweighted bipartite graph to an integral matching of nearly the same value in…
We initiate the study of approximate maximum matching in the vertex partition model, for graphs subject to dynamic changes. We assume that the $n$ vertices of the graph are partitioned among $k$ players, who execute a distributed algorithm…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…