arXiv subjects

Justine Cauvi

Publications and source records attributed to Justine Cauvi.

3 recordsLinked to original sources

arXiv2026

Designing sparse temporal graphs satisfying connectivity requirements

Connectivity of temporal graphs has been widely studied both as graph theory and as gossip theory. In particular, it is well known that in order to connect every vertex to every other, a temporal graph needs to have at least $2n-4$ edges where $n$ is the number of vertices. This paper investigates the optimal number of edges required to satisfy partial connectivity requirements. We introduce the problem of Connectivity Request Satisfaction where we are given a directed graph that we call the request graph, where an arc from $u$ to $v$ means that we need to be able to go from $u$ to $v$. Our goal is to build a temporal graph on the same vertex set with as few temporal edges as possible that would satisfy all the requests. When the graph we build is directed, we prove that the number of temporal arcs required is $n-\mathrm{cc}+\mathrm{dfvs}$ where $\mathrm{cc}$ is the number of connected component of the request graph and $\mathrm{dfvs}$ is the size of its smallest directed feedback vertex set. It follows that the problem is NP-complete but inherits fixed parameter tractability properties of Directed Feedback Vertex Set. When the graph we build is undirected, we establish a characterization of strongly connected request graphs that admit a solution with $n-1$ edges: it is possible if and only if any set of pairwise non-vertex-disjoint closed walks all share a common vertex. We prove that this criteria can be tested in polynomial time.

cs.DS↗

arXiv2025

Foremost, Fastest, Shortest: Temporal Graph Realization under Various Path Metrics

In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P . We consider the problems where as property P , we are given a prescribed matrix for the duration, length, or earliest arrival time of pairwise temporal paths. That is, we are given a matrix D and ask whether there is a temporal graph such that for any ordered pair of vertices (s, t), Ds,t equals the duration (length, or earliest arrival time, respectively) of any temporal path from s to t minimizing that specific temporal path metric. For shortest and earliest arrival temporal paths, we are the first to consider these problems as far as we know. We analyze these problems for many settings like: strict and non-strict paths, periodic and non-periodic temporal graphs, and limited number of labels per edge (that is, limited occurrence number per edge over time). In contrast to all other path metrics, we show that for the earliest arrival times, we can achieve polynomial-time algorithms in periodic and non-periodic temporal graphs and for strict and and non-strict paths. However, the problem becomes NP-hard when the matrix does not contain a single integer but a set or range of possible allowed values. As we show, the problem can still be solved efficiently in this scenario, when the number of entries with more than one value is small, that is, we develop an FPT-algorithm for the number of such entries. For the setting of fastest paths, we achieve new hardness results that answers an open question by Klobas, Mertzios, Molter, and Spirakis [Theor. Comput. Sci. '25] about the parameterized complexity of the problem with respect to the vertex cover number and significantly improves over a previous hardness result for the feedback vertex set number. When considering shortest paths, we show that the periodic versions are polynomial-time solvable whereas the non-periodic versions become NP-hard.

cs.DS↗

arXiv2025

Parameterized Restless Temporal Path

Recently, Bumpus and Meeks introduced a purely temporal parameter, called vertex-interval-membership-width, which is promising for the design of fixed-parameter tractable (FPT) algorithms for vertex reachability problems in temporal graphs. We study this newly introduced parameter for the problem of restless temporal paths, in which the waiting time at each node is restricted. In this article, we prove that, in the interval model, where arcs are present for entire time intervals, finding a restless temporal path is NP-hard even if the vertex-interval-membership-width is equal to three. We exhibit FPT algorithms for the point model, where arcs are present at specific points in time, both with uniform delay one and arbitrary positive delays. In the latter case, this comes with a slight additional computational cost.

cs.CC↗