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We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…

Data Structures and Algorithms · Computer Science 2025-05-20 Shi Li , Chenyang Xu , Ruilong Zhang

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

The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…

Data Structures and Algorithms · Computer Science 2018-11-20 Wojciech Nadara

We consider (closed neighbourhood) packings and their generalization in graphs called limited packings. A vertex set X in a graph G is a k-limited packing if for any vertex $v\in V(G)$, $\left|N[v] \cap X\right| \le k$, where $N[v]$ is the…

Discrete Mathematics · Computer Science 2014-07-08 Andrei Gagarin , Vadim Zverovich

We study a general family of problems that form a common generalization of classic hitting (also referred to as covering or transversal) and packing problems. An instance of X-HitPack asks: Can removing k (deletable) vertices of a graph G…

Data Structures and Algorithms · Computer Science 2024-02-26 Jacob Focke , Fabian Frei , Shaohua Li , Dániel Marx , Philipp Schepper , Roohani Sharma , Karol Węgrzycki

Overlapping clustering problem is an important learning issue in which clusters are not mutually exclusive and each object may belongs simultaneously to several clusters. This paper presents a kernel based method that produces overlapping…

Machine Learning · Computer Science 2012-11-30 Chiheb-Eddine Ben N'Cir , Nadia Essoussi

For a fixed graph $H$, the $H$-Coloring problem asks whether a given graph admits an edge-preserving function from its vertex set to that of $H$. A seminal theorem of Hell and Ne\v{s}et\v{r}il asserts that the $H$-Coloring problem is…

Data Structures and Algorithms · Computer Science 2025-07-18 Yael Berkman , Ishay Haviv

An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The overlap number of a graph is the minimum number of elements…

Discrete Mathematics · Computer Science 2010-08-17 Bill Rosgen , Lorna Stewart

We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any…

Data Structures and Algorithms · Computer Science 2010-10-08 Fedor V. Fomin , Daniel Lokshtanov , Neeldhara Misra , Geevarghese Philip , Saket Saurabh

We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the…

Computational Complexity · Computer Science 2015-03-17 Hans L. Bodlaender , Bart M. P. Jansen , Stefan Kratsch

In this paper, we investigate the problem of (k,r)-core which intends to find cohesive subgraphs on social networks considering both user engagement and similarity perspectives. In particular, we adopt the popular concept of k-core to…

Social and Information Networks · Computer Science 2016-11-11 Fan Zhang , Ying Zhang , Lu Qin , Wenjie Zhang , Xuemin Lin

Given a hypergraph $H = (V,E)$, what is the smallest subset $X \subseteq V$ such that $e \cap X \neq \emptyset$ holds for all $e \in E$? This problem, known as the hitting set problem, is a basic problem in parameterized complexity theory.…

Computational Complexity · Computer Science 2018-01-03 Max Bannach , Till Tantau

Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…

Social and Information Networks · Computer Science 2020-04-21 Jimit Majmudar , Stephen Vavasis

In $k$-hypergraph matching, we are given a collection of sets of size at most $k$, each with an associated weight, and we seek a maximum-weight subcollection whose sets are pairwise disjoint. More generally, in $k$-hypergraph $b$-matching,…

Data Structures and Algorithms · Computer Science 2016-04-04 Ojas Parekh , David Pritchard

For a class $\mathcal{G}$ of graphs, the problem SUBGRAPH COMPLEMENT TO $\mathcal{G}$ asks whether one can find a subset $S$ of vertices of the input graph $G$ such that complementing the subgraph induced by $S$ in $G$ results in a graph in…

Data Structures and Algorithms · Computer Science 2021-03-05 Dhanyamol Antony , Jay Garchar , Sagartanu Pal , R. B. Sandeep , Sagnik Sen , R. Subashini

In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…

Data Structures and Algorithms · Computer Science 2011-02-28 Marek Cygan , Fabrizio Grandoni , Stefano Leonardi , Marcin Mucha , Marcin Pilipczuk , Piotr Sankowski

Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization…

Data Structures and Algorithms · Computer Science 2015-03-19 Hans L. Bodlaender , Bart M. P. Jansen , Stefan Kratsch

Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…

Data Structures and Algorithms · Computer Science 2018-12-04 Tanmay Inamdar , Kasturi Varadarajan

K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using…

Social and Information Networks · Computer Science 2012-05-02 Fergal Reid , Aaron McDaid , Neil Hurley

In the $k$-Leaf Out-Branching and $k$-Internal Out-Branching problems we are given a directed graph $D$ with a designated root $r$ and a nonnegative integer $k$. The question is to determine the existence of an outbranching rooted at $r$…

Data Structures and Algorithms · Computer Science 2015-09-08 Marthe Bonamy , Łukasz Kowalik , Michał Pilipczuk , Arkadiusz Socała