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We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in…
Particle-based methods include a variety of techniques, such as Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC), for approximating a probabilistic target distribution with a set of weighted particles. In this paper, we…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
The edit distance of two strings is the minimum number of insertions, deletions, and substitutions of characters needed to transform one string into the other. The textbook dynamic-programming algorithm computes the edit distance of two…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
We obtain the first near-linear time deterministic algorithm for negative-weight single-source shortest paths on integer-weighted graphs. Our main ingredient is a deterministic construction of a padded decomposition on directed graphs,…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments,…
Given a set of numbers, the $k$-SUM problem asks for a subset of $k$ numbers that sums to zero. When the numbers are integers, the time and space complexity of $k$-SUM is generally studied in the word-RAM model; when the numbers are reals,…
Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \times B$ so that any point of $A \cup B$ appears in…
Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…
We introduce an algorithm for the minimization of deterministic Kripke structures with O(kn log2 n) time complexity. We prove the correctness and complexity properties of this algorithm.
We present a simple universal algorithm for high-dimensional integration which has the optimal error rate (independent of the dimension) in all weighted Korobov classes both in the randomized and the deterministic setting. Our theoretical…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
We present new algorithms for computing many faces in arrangements of lines and segments. Given a set $S$ of $n$ lines (resp., segments) and a set $P$ of $m$ points in the plane, the problem is to compute the faces of the arrangements of…
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…
We give a {\em deterministic} algorithm for approximately computing the fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter $\eps >…
A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that…
A modified dynamic programming algorithm rapidly and accurately solves large 0/1 knapsack problems. It has computational O(nlogn), space O(nlogn) and predictable maximum error. Experimentally it's accuracy increases faster than linearly…
Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is…