Related papers: Fully Dynamic Euclidean Bi-Chromatic Matching in S…
In this paper, we present a linear-time approximation scheme for $k$-means clustering of \emph{incomplete} data points in $d$-dimensional Euclidean space. An \emph{incomplete} data point with $\Delta>0$ unspecified entries is represented as…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
Dynamic stereo matching is the task of estimating consistent disparities from stereo videos with dynamic objects. Recent learning-based methods prioritize optimal performance on a single stereo pair, resulting in temporal inconsistencies.…
We propose a novel method for comparing non-aligned graphs of different sizes, based on the Wasserstein distance between graph signal distributions induced by the respective graph Laplacian matrices. Specifically, we cast a new formulation…
In the (fully) dynamic set cover problem, we have a collection of $m$ sets from a universe of size $n$ that undergo element insertions and deletions; the goal is to maintain an approximate set cover of the universe after each update. We…
We consider the dynamic graph coloring problem restricted to the class of interval graphs. At each update step the algorithm is presented with an interval to be colored, or a previously colored interval to delete. The goal of the algorithm…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
Given a dynamic graph $G$ with $n$ vertices and $m$ edges subject to insertion an deletions of edges, we show how to maintain a $(1+\varepsilon)\Delta$-edge-colouring of $G$ without the use of randomisation. More specifically, we show a…
We propose a numerical algorithm for computing approximately optimal solutions of the matching for teams problem. Our algorithm is efficient for problems involving large number of agent categories and allows for non-discrete agent type…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
Given a graph $G=(V,E)$ with costs on its edges, the minimum-cost edge cover problem consists of finding a subset of $E$ covering all vertices in $V$ at minimum cost. If $G$ is bipartite, this problem can be solved in time $O(|V|^3)$ via a…
Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…
Clustering is an important task with applications in many fields of computer science. We study the fully dynamic setting in which we want to maintain good clusters efficiently when input points (from a metric space) can be inserted and…
Baswana, Gupta and Sen [FOCS'11] showed that fully dynamic maximal matching can be maintained in general graphs with logarithmic amortized update time. More specifically, starting from an empty graph on $n$ fixed vertices, they devised a…
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 propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to…
We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph's arboricity, $\alpha$. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm…
We consider the problem of maintaining a proper $(\Delta + 1)$-vertex coloring in a graph on $n$-vertices and maximum degree $\Delta$ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time…
The first fully dynamic algorithm for maintaining a maximal independent set (MIS) with update time that is sublinear in the number of edges was presented recently by the authors of this paper [Assadi et.al. STOC'18]. The algorithm is…