Related papers: Near Optimal Subdivision Algorithms for Real Root …
We study the problem of approximating the largest root of a real-rooted polynomial of degree $n$ using its top $k$ coefficients and give nearly matching upper and lower bounds. We present algorithms with running time polynomial in $k$ that…
Structured pruning is an effective approach for compressing large pre-trained neural networks without significantly affecting their performance. However, most current structured pruning methods do not provide any performance guarantees, and…
Depth separation results propose a possible theoretical explanation for the benefits of deep neural networks over shallower architectures, establishing that the former possess superior approximation capabilities. However, there are no known…
We study the problem of explainable clustering in the setting first formalized by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). A $k$-clustering is said to be explainable if it is given by a decision tree where each internal node…
In the $k$-dispersion problem, we need to select $k$ nodes of a given graph so as to maximize the minimum distance between any two chosen nodes. This can be seen as a generalization of the independent set problem, where the goal is to…
We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with…
In the Distance-constrained Vehicle Routing Problem (DVRP), we are given a graph with integer edge weights, a depot, a set of $n$ terminals, and a distance constraint $D$. The goal is to find a minimum number of tours starting and ending at…
In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let $\lambda$ be the minimum cut. Our algorithm can compute $\lambda$ exactly in…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
We report our experiences for the development of a neighborhood algorithm implemented via tree-codes to optimize the performance of a discrete element method (DEM) for convex polytopes. Our implementation of the two-dimensional tree code…
We develop early stopping rules for growing regression tree estimators. The fully data-driven stopping rule is based on monitoring the global residual norm. The best-first search and the breadth-first search algorithms together with linear…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree…
The (unweighted) tree edit distance problem for $n$ node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in $O(n ^ 3)$ time [Demaine,…
We present two improved algorithms for weighted discrete $p$-center problem for tree networks with $n$ vertices. One of our proposed algorithms runs in $O(n \log n + p \log^2 n \log(n/p))$ time. For all values of $p$, our algorithm thus…
In this paper, multiple instance learning (MIL) algorithms to automatically perform root detection and segmentation in minirhizotron imagery using only image-level labels are proposed. Root and soil characteristics vary from location to…
We present a new and surprisingly simple analysis of random-shift decompositions -- originally proposed by Miller, Peng, and Xu [SPAA'13]: We show that decompositions for exponentially growing scales $D = 2^0, 2^1, \ldots,…
A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps : first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions…
Let $p\in\mathbb{Z}[x]$ be an arbitrary polynomial of degree $n$ with $k$ non-zero integer coefficients of absolute value less than $2^\tau$. In this paper, we answer the open question whether the real roots of $p$ can be computed with a…