Related papers: A Sub-Quadratic Exact Medoid Algorithm
A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
Tree edit distance is a well-studied measure of dissimilarity between rooted trees with node labels. It can be computed in $O(n^3)$ time [Demaine, Mozes, Rossman, and Weimann, ICALP 2007], and fine-grained hardness results suggest that the…
In this paper a new distributed asynchronous algorithm is proposed for time synchronization in networks with random communication delays, measurement noise and communication dropouts. Three different types of the drift correction algorithm…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
Given a distributed network represented by a weighted undirected graph $G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$ rounds, where $D$ is…
Two distributed algorithms are described that enable all users connected over a network to cooperatively solve the problem of minimizing the sum of all users' objective functions over the intersection of all users' constraint sets, where…
We consider the distributed optimization problem where $n$ agents each possessing a local cost function, collaboratively minimize the average of the $n$ cost functions over a connected network. Assuming stochastic gradient information is…
Gomory-Hu tree [Gomory and Hu, 1961] is a succinct representation of pairwise minimum cuts in an undirected graph. When the input graph has general edge weights, classic algorithms need at least cubic running time to compute a Gomory-Hu…
We present an approximation algorithm for computing the diameter of a point-set in $\Re^d$. The new algorithm is sensitive to the ``hardness'' of computing the diameter of the given input, and for most inputs it is able to compute the exact…
Edit distance is a measurement of similarity between two sequences such as strings, point sequences, or polygonal curves. Many matching problems from a variety of areas, such as signal analysis, bioinformatics, etc., need to be solved in a…
For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the…
Given a weighted and complete graph G = (V, E), V denotes the set of n objects to be clustered, and the weight d(u, v) associated with an edge (u, v) belonging to E denotes the dissimilarity between objects u and v. The diameter of a…
We show that any randomized first-order algorithm which minimizes a $d$-dimensional, $1$-Lipschitz convex function over the unit ball must either use $\Omega(d^{2-\delta})$ bits of memory or make $\Omega(d^{1+\delta/6-o(1)})$ queries, for…
In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an…
In the dynamic metric $k$-median problem, we wish to maintain a set of $k$ centers $S \subseteq V$ in an input metric space $(V, d)$ that gets updated via point insertions/deletions, so as to minimize the objective $\sum_{x \in V} \min_{y…
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the…
Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a…
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…