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We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted IDENTIFYING CODE, (OPEN) LOCATING-DOMINATING SET and METRIC DIMENSION) of an interval or a permutation graph. In…

Discrete Mathematics · Computer Science 2017-07-17 Florent Foucaud , George B. Mertzios , Reza Naserasr , Aline Parreau , Petru Valicov

In the NP-hard Edge Dominating Set problem (EDS) we are given a graph $G=(V,E)$ and an integer $k$, and need to determine whether there is a set $F\subseteq E$ of at most $k$ edges that are incident with all (other) edges of $G$. It is…

Data Structures and Algorithms · Computer Science 2019-01-14 Eva-Maria C. Hols , Stefan Kratsch

A set of vertices $W$ in a graph $G$ is called resolving if for any two distinct $x,y\in V(G)$, there is $v\in W$ such that ${\rm dist}_G(v,x)\neq{\rm dist}_G(v,y)$, where ${\rm dist}_G(u,v)$ denotes the length of a shortest path between…

Data Structures and Algorithms · Computer Science 2018-05-01 Gregory Gutin , M. S. Ramanujan , Felix Reidl , Magnus Wahlström

Minimum sum vertex cover of an $n$-vertex graph $G$ is a bijection $\phi : V(G) \to [n]$ that minimizes the cost $\sum_{\{u,v\} \in E(G)} \min \{\phi(u), \phi(v) \}$. Finding a minimum sum vertex cover of a graph (the MSVC problem) is…

Data Structures and Algorithms · Computer Science 2024-01-11 Shubhada Aute , Fahad Panolan

The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS'14) and Chitnis et al. (SODA'15 and SODA'16). Simply put, the main goal is to design streaming algorithms for parameterized problems…

Computational Complexity · Computer Science 2019-10-03 Arijit Bishnu , Arijit Ghosh , Sudeshna Kolay , Gopinath Mishra , Saket Saurabh

Many combinatorial problems can be solved in time $O^*(c^{tw})$ on graphs of treewidth $tw$, for a problem-specific constant $c$. In several cases, matching upper and lower bounds on $c$ are known based on the Strong Exponential Time…

Computational Complexity · Computer Science 2018-06-28 Bas A. M. van Geffen , Bart M. P. Jansen , Arnoud A. W. M. de Kroon , Rolf Morel

In a large-scale network, we want to choose some influential nodes to make a profit by paying some cost within a limited budget so that we do not have to spend more budget on some nodes adjacent to the chosen nodes; our problem is the…

Data Structures and Algorithms · Computer Science 2026-01-30 Sipra Singh

Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. This…

Data Structures and Algorithms · Computer Science 2025-10-07 Eduard Eiben , Diptapriyo Majumdar , M. S. Ramanujan

In this work we study the quantitative relation between VC-dimension and two other basic parameters related to learning and teaching. Namely, the quality of sample compression schemes and of teaching sets for classes of low VC-dimension.…

Machine Learning · Computer Science 2016-11-28 Shay Moran , Amir Shpilka , Avi Wigderson , Amir Yehudayoff

Cutwidth is a widely studied parameter that quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth…

Data Structures and Algorithms · Computer Science 2025-02-25 Narek Bojikian , Vera Chekan , Stefan Kratsch

The notion of $\mathcal{H}$-treewidth, where $\mathcal{H}$ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of $\mathcal{H}$-treewidth at most $k$…

Data Structures and Algorithms · Computer Science 2023-06-30 Bart M. P. Jansen , Jari J. H. de Kroon , Michal Wlodarczyk

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

We study the parameterized complexity of the classical Edge Hamiltonian Path problem and give several fixed-parameter tractability results. First, we settle an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT…

Data Structures and Algorithms · Computer Science 2014-03-11 Michael Lampis , Kazuhisa Makino , Valia Mitsou , Yushi Uno

The NP-hard 2-Club problem is, given an undirected graph G=(V,E) and l\in N, to decide whether there is a vertex set S\subseteq V of size at least l such that the induced subgraph G[S] has diameter at most two. We make progress towards a…

Computational Complexity · Computer Science 2013-05-17 Sepp Hartung , Christian Komusiewicz , André Nichterlein , Ondrej Suchý

We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…

Computational Geometry · Computer Science 2020-12-18 Mark de Berg , Hans L. Bodlaender , Sándor Kisfaludi-Bak , Dániel Marx , Tom C. van der Zanden

Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…

Data Structures and Algorithms · Computer Science 2025-01-27 Stefan Kratsch , Pascal Kunz

Clique-width is one of the most important parameters that describes structural complexity of a graph. Probably, only treewidth is more studied graph width parameter. In this paper we study how clique-width influences the complexity of the…

Data Structures and Algorithms · Computer Science 2020-03-11 Ivan Bliznets , Danil Sagunov

The tasks of extracting (top-$K$) Frequent Itemsets (FI's) and Association Rules (AR's) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running…

Data Structures and Algorithms · Computer Science 2015-03-19 Matteo Riondato , Eli Upfal

In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…

Data Structures and Algorithms · Computer Science 2023-02-02 Leon Kellerhals , Tomohiro Koana , Pascal Kunz , Rolf Niedermeier

We introduce the batched set cover problem, which is a generalization of the online set cover problem. In this problem, the elements of the ground set that need to be covered arrive in batches. Our main technical contribution is a tight…

Data Structures and Algorithms · Computer Science 2018-11-28 Juan C. Martínez Mori , Samitha Samaranayake