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We consider the minimum weight and smallest weight minimum-size dominating set problems in vertex-weighted graphs and networks. The latter problem is a two-objective optimization problem, which is different from the classic minimum weight…

Combinatorics · Mathematics 2024-01-23 Lukas Dijkstra , Andrei Gagarin , Vadim Zverovich

In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…

Optimization and Control · Mathematics 2016-04-20 Sergio Pequito , Guilherme Ramos , Soummya Kar , A. Pedro Aguiar , Jaime Ramos

We study the perfect matching lattice of a matching covered graph $G$, generated by the incidence vectors of its perfect matchings. Building on results of Lov\'asz and de Carvalho, Lucchesi, and Murty, we give a polynomial-time algorithm…

Combinatorics · Mathematics 2025-11-07 Olha Silina

We study minimum vertex cover problems on random \alpha-uniform hypergraphs using two different approaches, a replica method in statistical mechanics of random systems and a leaf removal algorithm. It is found that there exists a phase…

Disordered Systems and Neural Networks · Physics 2014-07-03 Satoshi Takabe , Koji Hukushima

The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…

Computational Complexity · Computer Science 2022-12-23 Hans-Jörg Kreowski , Sabine Kuske , Aaron Lye , Aljoscha Windhorst

We propose a \textit{purely combinatorial algorithm} for \mkvc{} in bipartite graphs, achieving approximation ratio~0.7. The only combinatorial algorithms currently known until now for this problem are the natural greedy algorithm, that…

Data Structures and Algorithms · Computer Science 2015-03-11 Vangelis Th. Paschos

In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…

Numerical Analysis · Mathematics 2021-01-25 Junyuan Lin , Guangpeng Ren

The parameterized complexity of problems is often studied with respect to the size of their optimal solutions. However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms parameterized by it…

Data Structures and Algorithms · Computer Science 2015-03-24 Meirav Zehavi

In this paper we study the generalized vertex cover problem (GVC), which is a generalization of various well studied combinatorial optimization problems. GVC is shown to be equivalent to the unconstrained binary quadratic programming…

Computational Complexity · Computer Science 2017-08-15 Pooja Pandey , Abraham P. Punnen

This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a…

Artificial Intelligence · Computer Science 2020-02-27 Marko Špoljarec , Robert Manger

In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms. Structural rounding works by first editing to a well-structured class, efficiently solving the edited instance, and…

Data Structures and Algorithms · Computer Science 2019-11-04 Brian Lavallee , Hayley Russell , Blair D. Sullivan , Andrew van der Poel

Given a graph $G$, the Connected Vertex Cover problem (CVC) asks to find a minimum cardinality vertex cover of $G$ that induces a connected subgraph. In this paper we describe some approaches to solve the CVC problem exactly. First, we give…

Data Structures and Algorithms · Computer Science 2023-02-20 Manuel Aprile

Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…

Data Structures and Algorithms · Computer Science 2018-11-08 Kaveh Khoshkhah , Mehdi Khosravian Ghadikolaei , Jerome Monnot , Florian Sikora

We review recent progress in the study of the vertex-cover problem (VC). VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC…

Disordered Systems and Neural Networks · Physics 2009-11-10 Alexander K. Hartmann , Martin Weigt

In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard…

Computational Geometry · Computer Science 2016-09-13 Washington Alves de Oliveira , Luiz Leduino de Salles Neto , Antonio Carlos Moretti , Ednei Felix Reis

We investigate the following above-guarantee parameterization of the classical Vertex Cover problem: Given a graph $G$ and $k\in\mathbb{N}$ as input, does $G$ have a vertex cover of size at most $(2LP-MM)+k$? Here $MM$ is the size of a…

Data Structures and Algorithms · Computer Science 2015-09-15 Shivam Garg , Geevarghese Philip

Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…

Discrete Mathematics · Computer Science 2023-05-17 Delia Garijo , Alberto Márquez , Rafael Robles

A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest matchings of $G$. In this paper, we present an algorithm for finding an optimal…

Combinatorics · Mathematics 2016-12-06 Xiumei Wang , Xiaoxin Song , Jinjiang Yuan

A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…

Data Structures and Algorithms · Computer Science 2025-12-05 Athanasios L. Konstantinidis , Charis Papadopoulos , Georgios Velissaris

We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…

Artificial Intelligence · Computer Science 2019-03-19 Yuu Jinnai , David Abel , D Ellis Hershkowitz , Michael Littman , George Konidaris