Related papers: A nearly optimal algorithm for deciding connectivi…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
This paper presents a new efficient algorithm which guarantees a solution for a class of multi-agent trajectory planning problems in obstacle-dense environments. Our algorithm combines the advantages of both grid-based and…
In this paper, we investigate the complexity of the central path of semidefinite optimization through the lens of real algebraic geometry. To that end, we propose an algorithm to compute real univariate representations describing the…
We consider the problem of efficiently solving a system of $n$ non-linear equations in ${\mathbb R}^d$. Addressing Smale's 17th problem stated in 1998, we consider a setting whereby the $n$ equations are random homogeneous polynomials of…
We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
We consider the problem of partitioning the edges of a graph into as few paths as possible. This is a~subject of the classic conjecture of Gallai and a recurring topic in combinatorics. Regarding the complexity of partitioning a graph…
We present a certified algorithm that takes a smooth algebraic curve in $\mathbb{R}^n$ and computes an isotopic approximation for a generic projection of the curve into $\mathbb{R}^2$. Our algorithm is designed for curves given implicitly…
We design new polynomial-time algorithms for recovering planted cliques in the semi-random graph model introduced by Feige and Kilian 2001. The previous best algorithms for this model succeed if the planted clique has size at least…
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
We describe a polynomial-time algorithm which, given a graph $G$ with treewidth $t$, approximates the pathwidth of $G$ to within a ratio of $O(t\sqrt{\log t})$. This is the first algorithm to achieve an $f(t)$-approximation for some…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both…
In the real world a graph is often fragmented and distributed across different sites. This highlights the need for evaluating queries on distributed graphs. This paper proposes distributed evaluation algorithms for three classes of queries:…
Motion planning in modified environments is a challenging task, as it compounds the innate difficulty of the motion planning problem with a changing environment. This renders some algorithmic methods such as probabilistic roadmaps less…
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set…