arXiv subjects

Sergio Thoumi

Publications and source records attributed to Sergio Thoumi.

5 recordsLinked to original sources

arXiv2025

On the Complexity of Claw-Free Vertex Splitting

Vertex splitting consists of taking a vertex $v$ in a graph and replacing it with two non-adjacent vertices whose combined neighborhoods is the neighborhood of $v$. The split is said to be exclusive when these neighborhoods are disjoint. In the Claw-Free (Exclusive) Vertex Splitting problem, we are given a graph $G$ and an integer $k$, and we are asked if we can perform at most $k$ (exclusive) vertex splits to obtain a claw-free graph. We consider the complexity of Claw-Free Exclusive Vertex Splitting and prove it to be NP-complete in general, while admitting a polynomial-time algorithm when the input graph has maximum degree 4. This result settles an open problem posed in [Firbas \& Sorge, ISAAC 2024]. We also show that our results can be generalized to $K_{1,c}$-Free Vertex Splitting for all $c \geq 3$.

cs.CC↗

arXiv2024

Correlation Clustering with Overlap: a Heuristic Graph Editing Approach

Correlation clustering seeks a partition of the vertex set of a given graph/network into groups of closely related, or just close enough, vertices so that elements of different groups are not close to each other. The problem has been previously modeled and studied as a graph editing problem, namely Cluster Editing, which assumes that closely related data elements must be adjacent. As such, the main objective (of the Cluster Editing problem) is to turn clusters into cliques as a way to identify them. This is to be obtained via two main edge editing operations: additions and deletions. There are two problems with the Cluster Editing model that we seek to address in this paper. First, ``closely'' related does not necessarily mean ``directly'' related. So closeness should be measured by relatively short distance. As such, we seek to turn clusters into (sub)graphs of small diameter. Second, in real applications, a data element can belong, or have roles, in multiple groups. In some cases, without allowing data elements to belong to more than one cluster each, makes it hard to achieve any clustering via classical partition-based methods. We address this latter problem by allowing vertex cloning, also known as vertex splitting. Heuristic methods for the introduced problem are presented along with experimental results showing the effectiveness of the proposed model and algorithmic approach.

cs.SI↗

arXiv2024

On the Complexity of 2-club Cluster Editing with Vertex Splitting

Editing a graph to obtain a disjoint union of s-clubs is one of the models for correlation clustering, which seeks a partition of the vertex set of a graph so that elements of each resulting set are close enough according to some given criterion. For example, in the case of editing into s-clubs, the criterion is proximity since any pair of vertices (in an s-club) are within a distance of s from each other. In this work we consider the vertex splitting operation, which allows a vertex to belong to more than one cluster. This operation was studied as one of the parameters associated with the Cluster Editing problem. We study the complexity and parameterized complexity of the s-Club Cluster Edge Deletion with Vertex Splitting and s-Club Cluster Vertex Splitting problems. Both problems are shown to be NP-Complete and APX-hard. On the positive side, we show that both problems are Fixed-Parameter Tractable with respect to the number of allowed editing operations and that s-Club Cluster Vertex Splitting is solvable in polynomial-time on the class of forests.

cs.DS↗

arXiv2023

Pack and Measure: An Effective Approach for Influence Propagation in Social Networks

The Influence Maximization problem under the Independent Cascade model (IC) is considered. The problem asks for a minimal set of vertices to serve as "seed set" from which a maximum influence propagation is expected. New seed-set selection methods are introduced based on the notions of a $d$-packing and vertex centrality. In particular, we focus on selecting seed-vertices that are far apart and whose influence-values are the highest in their local communities. Our best results are achieved via an initial computation of a $d$-Packing followed by selecting either vertices of high degree or high centrality in their respective closed neighborhoods. This overall "Pack and Measure" approach proves highly effective as a seed selection method.

cs.SI↗

arXiv2023

Concise Fuzzy Planar Embedding of Graphs: a Dimensionality Reduction Approach

The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However, rigorous edge storage might not always be essential to be able to draw the needed conclusions. A similar problem takes records with many variables and attempts to extract the most discernible features. It is said that the ``dimension'' of this data is reduced. Following an approach with the same objective in mind, we can map a graph representation to a $k$-dimensional space and answer queries of neighboring nodes mainly by measuring Euclidean distances. The accuracy of our answers would decrease but would be compensated for by fuzzy logic which gives an idea about the likelihood of error. This method allows for reasonable representation in memory while maintaining a fair amount of useful information, and allows for concise embedding in $k$-dimensional Euclidean space as well as solving some problems without having to decompress the graph. Of particular interest is the case where $k=2$. Promising highly accurate experimental results are obtained and reported.

cs.AI↗