English
Related papers

Related papers: The Parameterized Complexity of Clustering Incompl…

200 papers

The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for…

Combinatorics · Mathematics 2014-02-21 Henning Bruhn , Morgan Chopin , Felix Joos , Oliver Schaudt

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…

Computational Geometry · Computer Science 2015-02-18 Panos Giannopoulos , Christian Knauer , Gunter Rote , Daniel Werner

Deciding feasibility of large systems of linear equations and inequalities is one of the most fundamental algorithmic tasks. However, due to data inaccuracies or modeling errors, in practical applications one often faces linear systems that…

Data Structures and Algorithms · Computer Science 2022-09-07 Kristóf Bérczi , Alexander Göke , Lydia Mirabel Mendoza-Cadena , Matthias Mnich

We consider problems where the input is a set of points in the plane and an integer $k$, and the task is to find a subset $S$ of the input points of size $k$ such that $S$ satisfies some property. We focus on properties that depend only on…

Computational Geometry · Computer Science 2018-08-08 David Eppstein , Daniel Lokshtanov

The Cluster Editing problem seeks a transformation of a given undirected graph into a disjoint union of cliques via a minimum number of edge additions or deletions. A multi-parameterized version of the problem is studied, featuring a number…

Data Structures and Algorithms · Computer Science 2015-12-01 Faisal N. Abu-Khzam

In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a_1,\ldots,a_n} over \Sigma^m, where \Sigma is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median…

Data Structures and Algorithms · Computer Science 2021-04-19 Fedor V. Fomin , Petr A. Golovach , Nidhi Purohit

Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…

Data Structures and Algorithms · Computer Science 2008-02-14 Omid Amini , Fedor V. Fomin , Saket Saurabh

We study {\sc Cluster Edge Modification} problems with constraints on the size of the clusters. A graph $G$ is a cluster graph if every connected component of $G$ is a clique. In a typical {\sc Cluster Edge Modification} problem such as the…

Data Structures and Algorithms · Computer Science 2024-09-05 Jayakrishnan Madathil , Kitty Meeks

We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…

Computational Complexity · Computer Science 2024-11-26 Thomas Depian , Simon Dominik Fink , Alexander Firbas , Robert Ganian , Martin Nöllenburg

Graph Burning asks, given a graph $G = (V,E)$ and an integer $k$, whether there exists $(b_{0},\dots,b_{k-1}) \in V^{k}$ such that every vertex in $G$ has distance at most $i$ from some $b_{i}$. This problem is known to be NP-complete even…

Data Structures and Algorithms · Computer Science 2020-09-29 Yasuaki Kobayashi , Yota Otachi

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

Computational Complexity · Computer Science 2021-03-09 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…

Discrete Mathematics · Computer Science 2015-12-04 Jiří Fiala , Tomáš Gavenčiak , Dušan Knop , Martin Koutecký , Jan Kratochvíl

Clustering with incomplete views is a challenge in multi-view clustering. In this paper, we provide a novel and simple method to address this issue. Specifically, the proposed method simultaneously exploits the local information of each…

Computer Vision and Pattern Recognition · Computer Science 2018-09-18 Jie Wen , Zheng Zhang , Yong Xu , Zuofeng Zhong

Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently…

Data Structures and Algorithms · Computer Science 2024-07-16 Eduard Eiben , Robert Ganian , Iyad Kanj , Sebastian Ordyniak , Stefan Szeider

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…

Machine Learning · Computer Science 2022-10-18 Connor Lawless , Oktay Gunluk

The task of listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to…

Data Structures and Algorithms · Computer Science 2018-12-24 Matthias Bentert , Till Fluschnik , André Nichterlein , Rolf Niedermeier

In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…

Discrete Mathematics · Computer Science 2025-08-20 Nicole Schirrmacher , Sebastian Siebertz , Alexandre Vigny

The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…

Data Structures and Algorithms · Computer Science 2015-05-19 Michael R. Fellows , Serge Gaspers , Frances A. Rosamond

We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…

Data Structures and Algorithms · Computer Science 2020-08-19 Aritra Banik , Pratibha Choudhary , Venkatesh Raman , Saket Saurabh

We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a…

Data Structures and Algorithms · Computer Science 2022-10-25 Suhas Thejaswi , Ameet Gadekar , Bruno Ordozgoiti , Michal Osadnik