English
Related papers

Related papers: Improved Kernels for Edge Modification Problems

200 papers

In this paper we introduce a natural generalization of the well-known problems Cluster Editing and Bicluster Editing, whose parameterized versions have been intensively investigated in the recent literature. The generalized problem, called…

Data Structures and Algorithms · Computer Science 2015-06-03 Maise Dantas da Silva , Fábio Protti , Jayme Luiz Szwarcfiter

The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

Machine Learning · Statistics 2024-10-30 Aleksandr Talitckii , Brendon K. Colbert , Matthew M. Peet

Core decomposition is a fundamental operator in network analysis. In this paper, we study the problem of computing distance-generalized core decomposition on a network. A distance-generalized core, also termed $(k, h)$-core, is a maximal…

Data Structures and Algorithms · Computer Science 2021-10-25 Qiangqiang Dai , Rong-Hua Li , Lu Qin , Guoren Wang , Weihua Yang , Zhiwei Zhang , Ye Yuan

We study graph realization problems from a distributed perspective and we study it in the node capacitated clique (NCC) model of distributed computing, recently introduced for representing peer-to-peer networks. We focus on two central…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-19 John Augustine , Keerti Choudhary , Avi Cohen , David Peleg , Sumathi Sivasubramaniam , Suman Sourav

Vertex deletion to hereditary graph class is well-studied in parameterized complexity. Vertex deletion to the scattered graph classes has gained attention in recent years. In this paper, we consider (Proper-Interval, Tree)-Vertex Deletion,…

Data Structures and Algorithms · Computer Science 2026-05-05 Ashwin Jacob , Arpit Kumar , Diptapriyo Majumdar

The classical NP-complete problem Vertex Cover requires us to determine whether a graph contains at most $k$ vertices that cover all edges. In spite of its intractability, the problem can be solved in FPT time for parameter $k$ by various…

Data Structures and Algorithms · Computer Science 2018-07-31 Leizhen Cai

Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…

Data Structures and Algorithms · Computer Science 2019-05-28 Damir Ferizovic , Demian Hespe , Sebastian Lamm , Matthias Mnich , Christian Schulz , Darren Strash

A proper Helly circular-arc graph is an intersection graph of a set of arcs on a circle such that none of the arcs properly contains any other arc and every set of pairwise intersecting arcs has a common intersection. The Proper Helly…

Discrete Mathematics · Computer Science 2024-01-09 Akanksha Agrawal , Satyabrata Jana , Abhishek Sahu

Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses.…

Data Structures and Algorithms · Computer Science 2025-06-27 Fedor V. Fomin , Petr A. Golovach , Danil Sagunov , Kirill Simonov

In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a…

Discrete Mathematics · Computer Science 2018-01-09 Adèle Pass-Lanneau , Ayumi Igarashi , Frédéric Meunier

A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a…

The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…

Computational Complexity · Computer Science 2018-02-07 Bart M. P. Jansen , Astrid Pieterse

Over the last decade, the vertex-centric programming model has attracted significant attention in the world of graph processing, resulting in the emergence of a number of vertex-centric frameworks. Its simple programming interface, where…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-10-06 Ludovic Anthony Richard Capelli , Nick Brown , Jonathan Mark Bull

For a fixed graph $H$, in the List $H$-Coloring problem, we are given a graph $G$ along with list $L(v) \subseteq V(H)$ for every $v \in V(G)$, and we have to determine if there exists a list homomorphism $\varphi$ from $(G,L)$ to $H$,…

Combinatorics · Mathematics 2025-07-28 Marta Piecyk , Astrid Pieterse , Paweł Rzążewski , Magnus Wahlström

We study the existence of polynomial kernels, for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. Our main result is that a polynomial kernel for $k$-Dominating Set on…

Data Structures and Algorithms · Computer Science 2021-09-15 Édouard Bonnet , Eun Jung Kim , Amadeus Reinald , Stéphan Thomassé , Rémi Watrigant

Given a graph~$G$ and integers $k_1$, $k_2$, and~$k_3$, the unit interval editing problem asks whether $G$ can be transformed into a unit interval graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. We…

Data Structures and Algorithms · Computer Science 2017-01-03 Yixin Cao

We study the parameterized complexity of the T(h+1)-Free Edge Deletion problem. Given a graph G and integers k and h, the task is to delete at most k edges so that every connected component of the resulting graph has size at most h. The…

Data Structures and Algorithms · Computer Science 2026-02-04 Ajinkya Gaikwad , Soumen Maity , Leeja R

The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…

Computational Complexity · Computer Science 2026-02-24 Jakub Ruszil , Artur Polański , Adam Roman , Jakub Zelek

We consider a natural variant of the well-known Feedback Vertex Set problem, namely the problem of deleting a small subset of vertices or edges to a full binary tree. This version of the problem is motivated by real-world scenarios that are…

Data Structures and Algorithms · Computer Science 2020-01-01 Pratyush Dayal , Neeldhara Misra

Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…

Combinatorics · Mathematics 2014-09-09 Jed Yang