Related papers: On Approximate Fully-Dynamic Matching and Online M…
We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
We consider the Euclidean bi-chromatic matching problem in the dynamic setting, where the goal is to efficiently process point insertions and deletions while maintaining a high-quality solution. Computing the minimum cost bi-chromatic…
Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…
We give improved algorithms for maintaining edge-orientations of a fully-dynamic graph, such that the out-degree of each vertex is bounded. On one hand, we show how to orient the edges such that the out-degree of each vertex is proportional…
This paper studies a new online problem, referred to as \emph{min-cost perfect matching with delays (MPMD)}, defined over a finite metric space (i.e., a complete graph with positive edge weights obeying the triangle inequality)…
Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space…
Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is…
We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…
In this work, we study the trade-off between the running time of approximation algorithms and their approximation guarantees. By leveraging a structure of the `hard' instances of the Arora-Rao-Vazirani lemma [JACM'09], we show that the…
We study the problem of online unweighted bipartite matching with $n$ offline vertices and $n$ online vertices where one wishes to be competitive against the optimal offline algorithm. While the classic RANKING algorithm of Karp et al.…
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with…
We initiate the study of the submodular cover problem in dynamic setting where the elements of the ground set are inserted and deleted. In the classical submodular cover problem, we are given a monotone submodular function $f : 2^{V} \to…
Maximum bipartite matching (MBM) is a fundamental problem in combinatorial optimization with a long and rich history. A classic result of Hopcroft and Karp (1973) provides an $O(m \sqrt{n})$-time algorithm for the problem, where $n$ and $m$…
Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse…
We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the…
Randomized search heuristics such as evolutionary algorithms are frequently applied to dynamic combinatorial optimization problems. Within this paper, we present a dynamic model of the classic Weighted Vertex Cover problem and analyze the…
We initiate a systematic study on $\mathit{dynamic}$ $\mathit{influence}$ $\mathit{maximization}$ (DIM). In the DIM problem, one maintains a seed set $S$ of at most $k$ nodes in a dynamically involving social network, with the goal of…
A bipartite graph $G=(U,V,E)$ is convex if the vertices in $V$ can be linearly ordered such that for each vertex $u\in U$, the neighbors of $u$ are consecutive in the ordering of $V$. An induced matching $H$ of $G$ is a matching such that…
We present a deterministic incremental algorithm for \textit{exactly} maintaining the size of a minimum cut with $\widetilde{O}(1)$ amortized time per edge insertion and $O(1)$ query time. This result partially answers an open question…
We consider the Maximum-weight Matching (MWM) problem in the streaming sliding window model of computation. In this model, the input consists of a sequence of weighted edges on a given vertex set $V$ of size $n$. The objective is to…