Related papers: Improved Approximate Rips Filtrations with Shifted…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
A classic result of Williamson, Goemans, Mihail, and Vazirani [STOC 1993: 708-717] states that the problem of covering an uncrossable set family by a min-cost edge set admits approximation ratio $2$, by a primal-dual algorithm with a…
The long computational time and large memory requirements for computing Vietoris Rips persistent homology from point clouds remains a significant deterrent to its application to big data. This paper aims to reduce the memory footprint of…
The bilateral filter is a non-linear filter that uses a range filter along with a spatial filter to perform edge-preserving smoothing of images. A direct computation of the bilateral filter requires $O(S)$ operations per pixel, where $S$ is…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
Given a finite set $A\subset\mathbb{R}^d$, let Cov$_{r,k}$ denote the set of all points within distance $r$ to at least $k$ points of $A$. Allowing $r$ and $k$ to vary, we obtain a 2-parameter family of spaces that grow larger when $r$…
In the Two-Bar Charts Packing Problem (2-BCPP), it is required to pack the bar charts (BCs) consisting of two bars into the horizontal unit-height strip of minimal length. The bars may move vertically within the strip, but it is forbidden…
We present a new, inductive construction of the Vietoris-Rips complex, in which we take advantage of a small amount of unexploited combinatorial structure in the $k$-skeleton of the complex in order to avoid unnecessary comparisons when…
We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…
We prove that for each positive integer $n$, the Rips complexes of the $n$-dimensional integer lattice in the $d_1$ metric (i.e., the Manhattan metric, also called the natural word metric in the Cayley graph) are contractible at scales…
We consider approximation algorithms for covering integer programs of the form min $\langle c, x \rangle $ over $x \in \mathbb{N}^n $ subject to $A x \geq b $ and $x \leq d$; where $A \in \mathbb{R}_{\geq 0}^{m \times n}$, $b \in…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…
We show how to directly and efficiently approximate arbitrary one-qubit unitaries, bypassing the Euler decomposition and the magnitude approximation problem, at the cost of one ancillary qubit. Our technique also applies to approximating…
Independent set is a fundamental problem in combinatorial optimization. While in general graphs the problem is essentially inapproximable, for many important graph classes there are approximation algorithms known in the offline setting.…
Recent increase in the availability of warped images projected onto a manifold (e.g., omnidirectional spherical images), coupled with the success of higher-order assignment methods, has sparked an interest in the search for improved…
In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms. Structural rounding works by first editing to a well-structured class, efficiently solving the edited instance, and…
Given matrices A and B and vectors a, b, c and d, all with non-negative entries, we consider the problem of computing min {c.x: x in Z^n_+, Ax > a, Bx < b, x < d}. We give a bicriteria-approximation algorithm that, given epsilon in (0, 1],…
We present combinatorial approximation algorithms for the weighted correlation clustering problem. In this problem, we have a set of vertices and two weight values for each pair of vertices, denoting their difference and similarity. The…