相关论文: Shortest Dominating Set Reconfiguration under Toke…
This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…
Different variations of alliances in graphs have been introduced into the graph-theoretic literature about twenty years ago. More broadly speaking, they can be interpreted as groups that collaborate to achieve a common goal, for instance,…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
An arborescence, which is a directed analogue of a spanning tree in an undirected graph, is one of the most fundamental combinatorial objects in a digraph. In this paper, we study arborescences in digraphs from the viewpoint of…
In this paper, we study the {\sc Dominating Set} problem in random graphs. In a random graph, each pair of vertices are joined by an edge with a probability of $p$, where $p$ is a positive constant less than $1$. We show that, given a…
This paper describes a new alignment algorithm for sequences that can be used for determination of deletions and substitutions. It provides several solutions out of which the best one can be chosen on the basis of minimization of gaps or…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…
Node tokenized graph Transformers (GTs) have shown promising performance in node classification. The generation of token sequences is the key module in existing tokenized GTs which transforms the input graph into token sequences,…
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,…
LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…
Given two $k$-independent sets $I$ and $J$ of a graph $G$, one can ask if it is possible to transform the one into the other in such a way that, at any step, we replace one vertex of the current independent set by another while keeping the…
We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and…
Given a graph $G$ and an integer $k$, a token addition and removal ({\sf TAR} for short) reconfiguration sequence between two dominating sets $D_{\sf s}$ and $D_{\sf t}$ of size at most $k$ is a sequence $S= \langle D_0 = D_{\sf s}, D_1…
In a graph $G$, a vertex subset $S\subseteq V(G)$ is said to be a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A dominating set $S$ of a graph $G$ is called a paired-dominating set if the induced subgraph…
Problems from metric graph theory like Metric Dimension, Geodetic Set, and Strong Metric Dimension have recently had a strong impact in parameterized complexity by being the first known problems in NP to admit double-exponential lower…
We propose a new approach to interactive image segmentation based on some properties of a family of quadratic optimization problems related to dominant sets, a well-known graph-theoretic notion of a cluster which generalizes the concept of…
Dominating set problems are among the most important class of combinatorial problems in graph optimization, from a theoretical as well as from a practical point of view. In this paper, we address the recently introduced (minimum) weighted…
An st-shortest path, or st-path for short, in a graph G is a shortest (induced) path from s to t in G. Two st-paths are said to be adjacent if they differ on exactly one vertex. A reconfiguration sequence between two st-paths P and Q is a…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…