Related papers: Bicriteria Polygon Aggregation with Arbitrary Shap…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
Many combinatorial optimization problems can be approximated within $(1 \pm \epsilon)$ factors in $\text{poly}(\log n, 1/\epsilon)$ rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
Range aggregate queries find frequent application in data analytics. In some use cases, approximate results are preferred over accurate results if they can be computed rapidly and satisfy approximation guarantees. Inspired by a recent…
Suppose that a polygon $P$ is given as an array containing the vertices in counterclockwise order. We analyze how many vertices (including the index of each of these vertices) we need to know before we can bound $P$, i.e., report a bounded…
We want to recover the regression function in the single-index model. Using an aggregation algorithm with local polynomial estimators, we answer in particular to the second part of Question~2 from Stone (1982) on the optimal convergence…
Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Marin proposed a…
The aim of the paper is to propose a bounded-error quantum polynomial time (BQP) algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a…
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…
We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…
The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…
In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…
We consider inapproximability of the correlation clustering problem defined as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices…
Minimax designs provide a uniform coverage of a design space $\mathcal{X} \subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful…
Let $P$ be a polygon with $r>0$ reflex vertices and possibly with holes and islands. A subsuming polygon of $P$ is a polygon $P'$ such that $P \subseteq P'$, each connected component $R$ of $P$ is a subset of a distinct connected component…