相关论文: Dynamic Rank, Basis, and Matching
Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\"ive solution is to iteratively find the densest subgraph and remove it in…
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…
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…
Maximizing a monotone submodular function under cardinality constraint $k$ is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction,…
Dynamic algorithms come in three main flavors: $\mathit{incremental}$ (insertions-only), $\mathit{decremental}$ (deletions-only), or $\mathit{fully}$ $\mathit{dynamic}$ (both insertions and deletions). Fully dynamic is the holy grail of…
We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
We consider the maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition or deletion of edges. When the set of edges in a graph changes, we are interested in knowing the change in the set of…
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…
Graphs have been widely used in many applications such as social networks, collaboration networks, and biological networks. One important graph analytics is to explore cohesive subgraphs in a large graph. Among several cohesive subgraphs…
A finite dynamical system (FDS) is a system of multivariate functions over a finite alphabet, that is typically used to model a network of interacting entities. The main feature of a finite dynamical system is its interaction graph, which…
Detecting maximal square submatrices of ones in binary matrices is a fundamental problem with applications in computer vision and pattern recognition. While the standard dynamic programming (DP) solution achieves optimal asymptotic…
Ranking lists are often provided at regular time intervals in a range of applications, including economics, sports, marketing, and politics. Most popular methods for rank-order data postulate a linear specification for the latent scores,…
We present a deterministic fully dynamic algorithm with subpolynomial worst-case time per graph update such that after processing each update of the graph, the algorithm outputs a minimum cut of the graph if the graph has a cut of size at…
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…
Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…
We study geometric set cover problems in dynamic settings, allowing insertions and deletions of points and objects. We present the first dynamic data structure that can maintain an $O(1)$-approximation in sublinear update time for set cover…
A fundamental problem arising in many applications in Web science and social network analysis is, given an arbitrary approximation factor $c>1$, to output a set $S$ of nodes that with high probability contains all nodes of PageRank at least…
We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional…
Efficient consistency maintenance of incomplete and dynamic real-life databases is a quality label for further data analysis. In prior work, we tackled the generic problem of database updating in the presence of tuple generating constraints…
We propose a new method for shape recognition and retrieval based on dynamic programming. Our approach uses the dynamic programming algorithm to compute the optimal score and to find the optimal alignment between two strings. First, each…