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Directed graphs provide more subtle and precise modelling tools for optimization in road networks than simple graphs. In particular, they are more suitable in the context of alternative fuel vehicles and new automotive technologies, like…

Discrete Mathematics · Computer Science 2024-09-09 Lukas Dijkstra , Andrei Gagarin , Padraig Corcoran , Rhyd Lewis

Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…

Information Theory · Computer Science 2020-12-22 Yuval Shalev , Amichai Painsky , Irad Ben-Gal

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on…

Data Structures and Algorithms · Computer Science 2011-08-24 Mong-Jen Kao , D. T. Lee

A dominating set of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in set $S$. The corresponding optimization problem is known to be NP-hard. The best known…

Discrete Mathematics · Computer Science 2024-12-23 Ernesto Parra Inza , José María Sigarreta Almira , Nodari Vakhania

In this paper we deal with the signed Roman domination and signed total Roman domination problems. For each problem we propose two integer linear programming (ILP) formulations, the constraint programming (CP) formulation and variable…

Optimization and Control · Mathematics 2022-01-04 Vladimir Filipović , Dragan Matić , Aleksandar Kartelj

The \textsc{Dominating Set} problem is a classical and extensively studied topic in graph theory and theoretical computer science. In this paper, we examine the algorithmic complexity of several well-known exact-distance variants of…

Combinatorics · Mathematics 2026-03-03 Sandip Das , Sweta Das , Sk Samim Islam

Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…

Machine Learning · Statistics 2022-08-31 Etor Arza , Josu Ceberio , Ekhiñe Irurozki , Aritz Pérez

An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient…

Discrete Mathematics · Computer Science 2014-11-26 Andreas Brandstädt , Pavel Fičur , Arne Leitert , Martin Milanič

A {\em dominating set} of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in $S$. Finding a dominating set with the minimum cardinality in a connected graph…

Discrete Mathematics · Computer Science 2022-11-23 Frank Hernandez , Ernesto Parra , Jose Maria Sigarreta , Nodari Vakhania

The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…

Data Structures and Algorithms · Computer Science 2018-09-03 Michael A. Bekos , Henry Förster , Christian Geckeler , Lukas Holländer , Michael Kaufmann , Amadäus M. Spallek , Jan Splett

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

Roman domination is one of few examples where the related extension problem is polynomial-time solvable even if the original decision problem is NP-complete. This is interesting, as it allows to establish polynomial-delay enumeration…

Computational Complexity · Computer Science 2023-02-23 Henning Fernau , Kevin Mann

Let $G = (V,E)$ be a simple, undirected and connected graph. A connected (total) dominating set $S \subseteq V$ is a secure connected (total) dominating set of $G$, if for each $ u \in V \setminus S$, there exists $v \in S$ such that $uv…

Discrete Mathematics · Computer Science 2020-02-06 Jakkepalli Pavan Kumar , P. Venkata Subba Reddy , S. Arumugam

Given a positive integer $k$, a $k$-dominating set in a graph $G$ is a set of vertices such that every vertex not in the set has at least $k$ neighbors in the set. A total $k$-dominating set, also known as a $k$-tuple total dominating set,…

Data Structures and Algorithms · Computer Science 2018-07-25 Nina Chiarelli , Tatiana Romina Hartinger , Valeria Alejandra Leoni , Maria Inés Lopez Pujato , Martin Milanič

In $\textit{total domination}$, given a graph $G=(V,E)$, we seek a minimum-size set of nodes $S\subseteq V$, such that every node in $V$ has at least one neighbor in $S$. We define a $\textit{fault-tolerant}$ version of total domination,…

Data Structures and Algorithms · Computer Science 2026-03-11 Ioannis Lamprou , Ioannis Sigalas , Ioannis Vaxevanakis , Vassilis Zissimopoulos

In this paper we study three domination-like problems, namely identifying codes, locating-dominating codes, and locating-total-dominating codes. We are interested in finding the minimum cardinality of such codes in circular and infinite…

Discrete Mathematics · Computer Science 2017-08-03 Marwane Bouznif , Julien Darlay , Julien Moncel , Myriam Preissmann

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

Data Structures and Algorithms · Computer Science 2020-02-04 Kathrin Hanauer , Monika Henzinger , Christian Schulz

Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…

Data Structures and Algorithms · Computer Science 2015-02-20 Arindam Pal

We study the m-Eternal Domination problem, which is the following two-player game between a defender and an attacker on a graph: initially, the defender positions k guards on vertices of the graph; the game then proceeds in turns between…

Discrete Mathematics · Computer Science 2025-07-15 Tiziana Calamoneri , Federico Corò , Neeldhara Misra , Saraswati G. Nanoti , Giacomo Paesani

The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph coloring. In this paper we show that verifying whether the game…

Combinatorics · Mathematics 2016-06-20 Boštjan Brešar , Paul Dorbec , Sandi Klavžar , Gašper Košmrlj , Gabriel Renault