Related papers: Design of Dynamic Algorithms via Primal-Dual Metho…
Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main…
In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive…
We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes…
Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…
In this paper, we have developed a fully-dynamic algorithm for maintaining cardinality of maximum-matching in a tree using the construction of top-trees. The time complexities are as follows: 1. Initialization Time: $O(n(log(n)))$ to build…
We study dynamic algorithms for maintaining fundamental algebraic properties of matrices, specifically, rank, basis, and full-rank submatrices, with applications to maximum matching on dynamic graphs. Prior dynamic algorithms for rank…
We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of $n$ nodes is vertex-partitioned among $k$ players that…
The maximum coverage problem is to select $k$ sets from a collection of sets such that the cardinality of the union of the selected sets is maximized. We consider $(1-1/e-\epsilon)$-approximation algorithms for this NP-hard problem in three…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
This paper addresses the challenge of dynamic multi-objective optimization problems (DMOPs) by introducing novel approaches for accelerating prediction strategies within the evolutionary algorithm framework. Since the objectives of DMOPs…
The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage…
Most of real-world graphs are dynamic, i.e., they change over time by a sequence of update operations. While the regression problem has been studied for static graphs and temporal graphs, it is not investigated for general dynamic graphs.…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon,…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
We study dynamic algorithms for the problem of maximizing a monotone submodular function over a stream of $n$ insertions and deletions. We show that any algorithm that maintains a $(0.5+\epsilon)$-approximate solution under a cardinality…