Related papers: Multiway Cut, Pairwise Realizable Distributions, a…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
We consider the weighted $k$-set packing problem, in which we are given a collection of weighted sets, each with at most $k$ elements and must return a collection of pairwise disjoint sets with maximum total weight. For $k = 3$, this…
Unconstrained submodular maximization captures many NP-hard combinatorial optimization problems, including Max-Cut, Max-Di-Cut, and variants of facility location problems. Recently, Buchbinder et al. presented a surprisingly simple linear…
$k$-Coloring Reconfiguration is one of the most well-studied reconfiguration problems, which asks to transform a given proper $k$-coloring of a graph to another by repeatedly recoloring a single vertex. Its approximate version, Maxmin…
In the maximum independent set of convex polygons problem, we are given a set of $n$ convex polygons in the plane with the objective of selecting a maximum cardinality subset of non-overlapping polygons. Here we study a special case of the…
In this paper, we prove that the Max-Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch. We describe two different approximation algorithms for the Max-Morse Matching Problem. For…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
Due to hybridization events in evolution, studying two different genes of a set of species may yield two related but different phylogenetic trees for the set of species. In this case, we want to measure the dissimilarity of the two trees.…
The n-way number partitioning problem, a fundamental challenge in combinatorial optimization, has significant implications for applications such as fair division and machine scheduling. Despite these problems being NP-hard, many…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
In this paper, we study several generalizations of multiway cut where the terminals can be chosen as \emph{representatives} from sets of \emph{candidates} $T_1,\ldots,T_q$. In this setting, one is allowed to choose these representatives so…
Correlation Clustering is a classic clustering objective arising in numerous machine learning and data mining applications. Given a graph $G=(V,E)$, the goal is to partition the vertex set into clusters so as to minimize the number of edges…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
By first solving the equation $x^3+y^3+z^3=k$ with fixed $k$ for $z$ and then considering the distance to the nearest integer function of the result, we turn the sum of three cubes problem into an optimisation one. We then apply three…
Max-Cut is a classical graph-partitioning problem where given a graph $G = (V,E)$, the objective is to find a cut $(S,S^c)$ which maximizes the number of edges crossing the cut. In a seminal work, Goemans and Williamson gave an $\alpha_{GW}…
We show that there is no $(1+\eps)$-approximation algorithm for the problem of covering points in the plane by minimum number of fat triangles of similar size (with the minimum angle of the triangles being close to 45 degrees). Here, the…
We propose to generate Lagrangian cut for two-stage stochastic integer program by batch, in contrast to the existing methods which solve each Lagrangian subproblem at every iteration. We establish two convergence properties of the proposed…
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…