arXiv subjects

Anne-Sophie Himmel

Publications and source records attributed to Anne-Sophie Himmel.

7 recordsLinked to original sources

arXiv2021

The Computational Complexity of Finding Temporal Paths under Waiting Time Constraints

Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes over time, gained more and more attention. A path is time-respecting, or temporal, if it uses edges with non-decreasing time stamps. We investigate a basic constraint for temporal paths, where the time spent at each vertex must not exceed a given duration $Δ$, referred to as $Δ$-restless temporal paths. This constraint arises naturally in the modeling of real-world processes like packet routing in communication networks and infection transmission routes of diseases where recovery confers lasting resistance. While finding temporal paths without waiting time restrictions is known to be doable in polynomial time, we show that the "restless variant" of this problem becomes computationally hard even in very restrictive settings. For example, it is W[1]-hard when parameterized by the distance to disjoint path of the underlying graph, which implies W[1]-hardness for many other parameters like feedback vertex number and pathwidth. A natural question is thus whether the problem becomes tractable in some natural settings. We explore several natural parameterizations, presenting FPT algorithms for three kinds of parameters: (1) output-related parameters (here, the maximum length of the path), (2) classical parameters applied to the underlying graph (e.g., feedback edge number), and (3) a new parameter called timed feedback vertex number, which captures finer-grained temporal features of the input temporal graph, and which may be of interest beyond this work.

cs.DM↗

arXiv2020

Multistage Graph Problems on a Global Budget

Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one studies the different (time) layers of a temporal graph (effectively meaning that the edge set may change over time, but the vertex set remains unchanged), and one searches for a solution of a given graph problem for each layer. The twist in the multistage setting is that the solutions found must not differ too much between subsequent layers. We relax on this already established notion by introducing a global instead of the local budget view studied so far. More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is moderate. Studying several classical graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized complexity angle, we encounter both fixed-parameter tractability and parameterized hardness results. Somewhat surprisingly, we find that sometimes the global multistage versions of NP-hard problems such as Vertex Cover turn out to be computationally more tractable than the ones of polynomial-time solvable problems such as Matching.

cs.CC↗

arXiv2020

On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering

Editing a graph into a disjoint union of clusters is a standard optimization task in graph-based data clustering. Here, complementing classic work where the clusters shall be cliques, we focus on clusters that shall be 2-clubs, that is, subgraphs of diameter two. This naturally leads to the two NP-hard problems 2-Club Cluster Editing (the allowed editing operations are edge insertion and edge deletion) and 2-Club Cluster Vertex Deletion (the allowed editing operations are vertex deletions). Answering an open question from the literature, we show that 2-Club Cluster Editing is W[2]-hard with respect to the number of edge modifications, thus contrasting the fixed-parameter tractability result for the classic Cluster Editing problem (considering cliques instead of 2-clubs). Then focusing on 2-Club Cluster Vertex Deletion, which is easily seen to be fixed-parameter tractable, we show that under standard complexity-theoretic assumptions it does not have a polynomial-size problem kernel when parameterized by the number of vertex deletions. Nevertheless, we develop several effective data reduction and pruning rules, resulting in a competitive solver, clearly outperforming a standard CPLEX solver in most instances of an established biological test data set.

cs.DS↗

arXiv2020

Efficient Computation of Optimal Temporal Walks under Waiting-Time Constraints

Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into account the temporal aspect leads to a rich set of optimization criteria for "shortest" walks. Extending and significantly broadening state-of-the-art work of Wu et al. [IEEE TKDE 2016], we provide an algorithm for computing optimal walks that is capable to deal with various optimization criteria and any linear combination of these. It runs in $O (|V| + |E| \log |E|)$ time where $|V|$ is the number of vertices and $|E|$ is the number of time edges. A central distinguishing factor to Wu et al.'s work is that our model allows to, motivated by real-world applications, respect waiting-time constraints for vertices, that is, the minimum and maximum waiting time allowed in intermediate vertices of a walk. Moreover, other than Wu et al. our algorithm also allows to search for walks that pass multiple subsequent edges in one time step, and it can optimize a richer set of optimization criteria. Our experimental studies indicate that our richer modeling can be achieved without significantly worsening the running time when compared to Wu et al.'s algorithms.

cs.DS↗

arXiv2019

Listing All Maximal $k$-Plexes in Temporal Graphs

Many real-world networks evolve over time, that is, new contacts appear and old contacts may disappear. They can be modeled as temporal graphs where interactions between vertices (which represent people in the case of social networks) are represented by time-stamped edges. One of the most fundamental problems in (social) network analysis is community detection, and one of the most basic primitives to model a community is a clique. Addressing the problem of finding communities in temporal networks, Viard et al. [TCS 2016] introduced $Δ$-cliques as a natural temporal version of cliques. Himmel et al. [SNAM 2017] showed how to adapt the well-known Bron-Kerbosch algorithm to enumerate $Δ$-cliques. We continue this work and improve and extend the algorithm of Himmel et al. to enumerate temporal $k$-plexes (notably, cliques are the special case $k=1$). We define a $Δ$-$k$-plex as a set of vertices and a time interval, where during this time interval each vertex has in each consecutive $Δ+ 1$ time steps at least one edge to all but at most $k-1$ vertices in the chosen set of vertices. We develop a recursive algorithm for enumerating all maximal $Δ$-$k$-plexs and perform experiments on real-world social networks that demonstrate the practical feasibility of our approach. In particular, for the special case of $Δ$-1-plexes (that is, $Δ$-cliques), we observe that our algorithm is on average significantly faster than the previous algorithms by Himmel et al. [SNAM 2017] and Viard et al. [IPL 2018] for enumerating $Δ$-cliques.

cs.DS↗

arXiv2018

Computational Complexity Aspects of Point Visibility Graphs

A point visibility graph is a graph induced by a set of points in the plane where the vertices of the graph represent the points in the point set and two vertices are adjacent if and only if no other point from the point set lies on the line segment between the two corresponding points. The set of all point visibility graphs form a graph class which is examined from a computational complexity perspective in this paper. We show NP-hardness for several classic graph problems on point visibility graphs such as Feedback Vertex Set, Longest Induced Path, Bisection and $\mathcal{F}$-free Vertex Deletion (for certain sets $\mathcal{F}$). Furthermore, we consider the complexity of the Dominating Set problem on point visibility graphs of points on a grid.

cs.DM↗

arXiv2017

Adapting the Bron-Kerbosch Algorithm for Enumerating Maximal Cliques in Temporal Graphs

Dynamics of interactions play an increasingly important role in the analysis of complex networks. A modeling framework to capture this are temporal graphs which consist of a set of vertices (entities in the network) and a set of time-stamped binary interactions between the vertices. We focus on enumerating delta-cliques, an extension of the concept of cliques to temporal graphs: for a given time period delta, a delta-clique in a temporal graph is a set of vertices and a time interval such that all vertices interact with each other at least after every delta time steps within the time interval. Viard, Latapy, and Magnien [ASONAM 2015, TCS 2016] proposed a greedy algorithm for enumerating all maximal delta-cliques in temporal graphs. In contrast to this approach, we adapt the Bron-Kerbosch algorithm - an efficient, recursive backtracking algorithm which enumerates all maximal cliques in static graphs - to the temporal setting. We obtain encouraging results both in theory (concerning worst-case running time analysis based on the parameter "delta-slice degeneracy" of the underlying graph) as well as in practice with experiments on real-world data. The latter culminates in an improvement for most interesting delte-values concerning running time in comparison with the algorithm of Viard, Latapy, and Magnien.

cs.DS↗