相关论文: Discrete-time treatment number

Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…

Given a population with dynamic pairwise connections, we ask if the entire population could be (indirectly) infected by a small group of $k$ initially infected individuals. We formalise this problem as the Temporal Reachability Dominating…

For intractable problems on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained complexity results. Although the studies in this direction are successful, we still need a…

An isolating set of a graph is a set of vertices $S$ such that, if $S$ and its neighborhood is removed, only isolated vertices remain; and the isolation number is the minimum size of such a set. It is known that for every connected graph…

An obstacle representation of a graph $G$ is a set of points in the plane representing the vertices of $G$, together with a set of polygonal obstacles such that two vertices of $G$ are connected by an edge in $G$ if and only if the line…

Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…

Foucaud et al. [Discrete Appl. Math. 319 (2022), 424-438] recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. For a set $M$ of vertices and an edge $e$ of a graph $G$, let $P(M,…

$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…

We study differentially private algorithms for analyzing graphs in the challenging setting of continual release with fully dynamic updates, where edges are inserted and deleted over time, and the algorithm is required to update the solution…

In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the…

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…

Through legislation and technical advances users gain more control over how their data is processed, and they expect online services to respect their privacy choices and preferences. However, data may be processed for many different…

Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…

We study the fine-grained complexity of graph connectivity problems in unweighted undirected graphs. Recent development shows that all variants of edge connectivity problems, including single-source-single-sink, global, Steiner,…

We study how to sparsify connectivity in graphs under a tight deletion budget. Given a graph $G$ and integers $k,x \ge 0$, Critical Node Cut (CNC) asks whether we can delete at most $k$ vertices so that the number of remaining unordered…

A temporal graph is a graph in which the edge set can change from one time step to the next. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk…

The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…

For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…

We study the distributed message-passing model in which a communication network is represented by a graph G=(V,E). Usually, the measure of complexity that is considered in this model is the worst-case complexity, which is the largest number…

A temporal graph is a finite sequence of graphs, called snapshots, over the same vertex set. Many temporal graph problems turn out to be much more difficult than their static counterparts. One such problem is \textsc{Timeline Vertex Cover}…