arXiv subjects

Athanasios L. Konstantinidis

Publications and source records attributed to Athanasios L. Konstantinidis.

8 recordsLinked to original sources

arXiv2025

Algorithms and Complexity of Hedge Cluster Deletion Problems

A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the minimum number of hedges of a hedge graph so that their removal results in a graph that is isomorphic to a disjoint union of cliques. We identify NP-completeness and polynomial-time solutions based on vertex-disjoint 3-vertex-paths as subgraphs. Regarding its approximability, we show that it is NP-hard to approximate \textsc{Hedge Cluster Deletion} within factor $2^{O(\log^{1-\epsilon} r)}$ for any $\epsilon >0$, where $r$ is the number of hedges in a given hedge graph. While \textsc{Hedge Cluster Deletion} is fixed-parameter tractable with respect to the solution size (i.e., the number of removal hedges), we prove that it does not admit a polynomial kernel, unless NP $\subseteq$ coNP/poly. Moreover, we consider the hedge underlying structure. We give a polynomial-time algorithm with constant approximation ratio for \textsc{Hedge Cluster Deletion} whenever each triangle of the input graph is covered by at most two hedges. On the way to this result, an interesting ingredient that we solved efficiently is a variant of the \textsc{Vertex Cover} problem in which apart from the desired vertex set that covers the edge set, a given set of vertex-constraints should also be included in the solution. Moreover, as a possible workaround for the existence of efficient exact algorithms, we propose the hedge intersection graph which is the intersection graph spanned by the hedges. Towards this direction, we give a polynomial-time algorithm for \textsc{Hedge Cluster Deletion} whenever the hedge intersection graph is acyclic.

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arXiv2025

Local Clustering in Hypergraphs through Higher-Order Motifs

Hypergraphs provide a powerful framework for modeling complex systems and networks with higher-order interactions beyond simple pairwise relationships. However, graph-based clustering approaches, which focus primarily on pairwise relations, fail to represent higher-order interactions, often resulting in low-quality clustering outcomes. In this work, we introduce a novel approach for local clustering in hypergraphs based on higher-order motifs, small connected subgraphs in which nodes may be linked by interactions of any order, extending motif-based techniques previously applied to standard graphs. Our method exploits hypergraph-specific higher-order motifs to better characterize local structures and optimize motif conductance. We propose two alternative strategies for identifying local clusters around a seed hyperedge: a core-based method utilizing hypergraph core decomposition and a BFS-based method based on breadth-first exploration. We construct an auxiliary hypergraph to facilitate efficient partitioning and introduce a framework for local motif-based clustering. Extensive experiments on real-world datasets demonstrate the effectiveness of our framework and provide a comparative analysis of the two proposed clustering strategies in terms of clustering quality and computational efficiency.

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arXiv2024

Consistent Tie-Strength Labeling for Multilayer Strong Triadic Closure

Inferring tie strengths (strong vs. weak) is a core task in network analysis, often guided by the Strong Triadic Closure (STC) principle. In multilayer networks, such as social platforms or biological systems, applying STC independently to each layer can lead to inconsistent tie labels, undermining interpretations that rely on coherent relationship semantics across layers. We propose new formulations, multilayer STC and its extension STC+, which are axiomatically grounded and enforce cross-layer consistency. These problems are NP-hard; we present efficient 2- and 6-approximation algorithms alongside exact solutions. Experiments on real-world networks demonstrate that our methods produce consistent tie strength labelings with a transparent structural justification, significantly improving over the baselines.

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arXiv2024

Online Drone Scheduling for Last-mile Delivery

Delivering a parcel from the distribution hub to the customer's doorstep is called the \textit{last-mile delivery} step in delivery logistics. In this paper, we study a hybrid {\it truck-drones} model for the last-mile delivery step, in which a truck moves on a predefined path carrying parcels and drones deliver the parcels. We define the \textsc{online drone scheduling} problem, where the truck moves in a predefined path, and the customer's requests appear online during the truck's movement. The objective is to schedule a drone associated with every request to minimize the number of drones used subject to the battery budget of the drones and compatibility of the schedules. We propose a 3-competitive deterministic algorithm using the next-fit strategy and 2.7-competitive algorithms using the first-fit strategy for the problem with $O(\log n)$ worst-case time complexity per request, where $n$ is the maximum number of active requests at any time. We also introduce \textsc{online variable-size drone scheduling} problem (OVDS). Here, we know all the customer's requests in advance; however, the drones with different battery capacities appear online. The objective is to schedule customers' requests for drones to minimize the number of drones used. We propose a $(2α+ 1)$-competitive algorithm for the OVDS problem with total running time $O(n \log n)$ for $n$ customer requests, where $α$ is the ratio of the maximum battery capacity to the minimum battery capacity of the drones. Finally, we address how to generate intervals corresponding to each customer request when there are discrete stopping points on the truck's route, from where the drone can fly and meet with the truck.

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arXiv2024

Inferring Tie Strength in Temporal Networks

Inferring tie strengths in social networks is an essential task in social network analysis. Common approaches classify the ties as wea} and strong ties based on the strong triadic closure (STC). The STC states that if for three nodes, $A$, $B$, and $C$, there are strong ties between $A$ and $B$, as well as $A$ and $C$, there has to be a (weak or strong) tie between $B$ and $C$. A variant of the STC called STC+ allows adding a few new weak edges to obtain improved solutions. So far, most works discuss the STC or STC+ in static networks. However, modern large-scale social networks are usually highly dynamic, providing user contacts and communications as streams of edge updates. Temporal networks capture these dynamics. To apply the STC to temporal networks, we first generalize the STC and introduce a weighted version such that empirical a priori knowledge given in the form of edge weights is respected by the STC. Similarly, we introduce a generalized weighted version of the STC+. The weighted STC is hard to compute, and our main contribution is an efficient 2-approximation (resp. 3-approximation) streaming algorithm for the weighted STC (resp. STC+) in temporal networks. As a technical contribution, we introduce a fully dynamic $k$-approximation for the minimum weighted vertex cover problem in hypergraphs with edges of size $k$, which is a crucial component of our streaming algorithms. An empirical evaluation shows that the weighted STC leads to solutions that better capture the a priori knowledge given by the edge weights than the non-weighted STC. Moreover, we show that our streaming algorithm efficiently approximates the weighted STC in real-world large-scale social networks.

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arXiv2023

An Edge-Based Decomposition Framework for Temporal Networks

A temporal network is a dynamic graph where every edge is assigned an integer time label that indicates at which discrete time step the edge is available. We consider the problem of hierarchically decomposing the network and introduce an edge-based decomposition framework that unifies the core and truss decompositions for temporal networks while allowing us to consider the network's temporal dimension. Based on our new framework, we introduce the $(k,\Delta)$-core and $(k,\Delta)$-truss decompositions, which are generalizations of the classic $k$-core and $k$-truss decompositions for multigraphs. Moreover, we show how $(k,\Delta)$-cores and $(k,\Delta)$-trusses can be efficiently further decomposed to obtain spatially and temporally connected components. We evaluate the characteristics of our new decompositions and the efficiency of our algorithms. Moreover, we demonstrate how our $(k,\Delta)$-decompositions can be applied to analyze malicious content in a Twitter network to obtain insights that state-of-the-art baselines cannot obtain.

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arXiv2019

Cluster Deletion on Interval Graphs and Split Related Graphs

In the {\sc Cluster Deletion} problem the goal is to remove the minimum number of edges of a given graph, such that every connected component of the resulting graph constitutes a clique. It is known that the decision version of {\sc Cluster Deletion} is NP-complete on ($P_5$-free) chordal graphs, whereas {\sc Cluster Deletion} is solved in polynomial time on split graphs. However, the existence of a polynomial-time algorithm of {\sc Cluster Deletion} on interval graphs, a proper subclass of chordal graphs, remained a well-known open problem. Our main contribution is that we settle this problem in the affirmative, by providing a polynomial-time algorithm for {\sc Cluster Deletion} on interval graphs. Moreover, despite the simple formulation of the algorithm on split graphs, we show that {\sc Cluster Deletion} remains NP-complete on a natural and slight generalization of split graphs that constitutes a proper subclass of $P_5$-free chordal graphs. To complement our results, we provide two polynomial-time algorithms for {\sc Cluster Deletion} on subclasses of such generalizations of split graphs.

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arXiv2018

Parameterized Aspects of Strong Subgraph Closure

Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study of the Strong F-closure problem, where F is a fixed graph. This is a generalization of Strong Triadic Closure, whereas it is a relaxation of F-free Edge Deletion. In Strong F-closure, we want to select a maximum number of edges of the input graph G, and mark them as strong edges, in the following way: whenever a subset of the strong edges forms a subgraph isomorphic to F, then the corresponding induced subgraph of G is not isomorphic to F. Hence the subgraph of G defined by the strong edges is not necessarily F-free, but whenever it contains a copy of F, there are additional edges in G to destroy that strong copy of F in G. We study Strong F-closure from a parameterized perspective with various natural parameterizations. Our main focus is on the number k of strong edges as the parameter. We show that the problem is FPT with this parameterization for every fixed graph F, whereas it does not admit a polynomial kernel even when F =P_3. In fact, this latter case is equivalent to the Strong Triadic Closure problem, which motivates us to study this problem on input graphs belonging to well known graph classes. We show that Strong Triadic Closure does not admit a polynomial kernel even when the input graph is a split graph, whereas it admits a polynomial kernel when the input graph is planar, and even d-degenerate. Furthermore, on graphs of maximum degree at most 4, we show that Strong Triadic Closure is FPT with the above guarantee parameterization k - μ(G), where μ(G) is the maximum matching size of G. We conclude with some results on the parameterization of Strong F-closure by the number of edges of G that are not selected as strong.

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