arXiv subjects

Fariba Ranjbar

Publications and source records attributed to Fariba Ranjbar.

7 recordsLinked to original sources

arXiv2026

Cluster deletion in cographs, permutation graphs, and graphs with bounded clique number

The Cluster Deletion problem asks for a minimum-size edge set whose deletion turns a graph into a disjoint union of complete graphs. Equivalently, the Clique Partition problem asks for a partition of the vertex set into cliques that maximizes the number of edges within the parts. We give a simpler proof of a result of Gao, Hare, and Nastos (Discete Mathematics, 2013), that Cluster Deletion is polynomial-time solvable on cographs. In addition, we show that the natural linear programming formulation of Clique Partition is exact on cographs. We then show that Cluster Deletion is NP-complete on permutation graphs, which are a superclass of cographs. This answers an open question of Konstantinidis and Papadopoulos (Algorithmica, 2021). We also exhibit a permutation graph on nine vertices for which the linear programming formulation is not exact. Finally, for graphs with clique number at most $c$, we give a polynomial-time $2\binom{c}{2}/(\binom{c}{2}+1)$-approximation algorithm for Clique Partition. More generally, the algorithm runs in polynomial time on every graph class for which a maximum clique can be found in polynomial time. For each fixed $c\geq 3$, we also construct infinitely many examples attaining the stated approximation ratio. The same examples show that, for Cluster Deletion , the algorithm is a $2$-approximation and no better, for every fixed $c \geq 3$.

cs.DS↗

arXiv2026

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.

cs.SI↗

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.

cs.SI↗

arXiv2021

Counting and localizing defective nodes by Boolean network tomography

Identifying defective items in larger sets is a main problem with many applications in real life situations. We consider the problem of localizing defective nodes in networks through an approach based on boolean network tomography (BNT), which is grounded on inferring informations from the boolean outcomes of end-to-end measurements paths. {\em Identifiability} conditions on the set of paths which guarantee discovering or counting unambiguously the defective nodes are of course very relevant. We investigate old and introduce new identifiability conditions contributing this problem both from a theoretical and applied perspective. (1) What is the precise tradeoff between number of nodes and number of paths such that at most $k$ nodes can be identified unambiguously ? The answer is known only for $k=1$ and we answer the question for any $k$, setting a problem implicitly left open in previous works. (2) We study upper and lower bounds on the number of unambiguously identifiable nodes, introducing new identifiability conditions which strictly imply and are strictly implied by unambiguous identifiability; (3) We use these new conditions on one side to design algorithmic heuristics to count defective nodes in a fine-grained way, on the other side to prove the first complexity hardness results on the problem of identifying defective nodes in networks via BNT. (4) We introduce a random model where we study lower bounds on the number of unambiguously identifiable defective nodes and we use this model to estimate that number on real networks by a maximum likelihood estimate approach

cs.NI↗

arXiv2019

Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography

We study maximal identifiability, a measure recently introduced in Boolean Network Tomography to characterize networks' capability to localize failure nodes in end-to-end path measurements. We prove tight upper and lower bounds on the maximal identifiability of failure nodes for specific classes of network topologies, such as trees and $d$-dimensional grids, in both directed and undirected cases. We prove that directed $d$-dimensional grids with support $n$ have maximal identifiability $d$ using $2d(n-1)+2$ monitors; and in the undirected case we show that $2d$ monitors suffice to get identifiability of $d-1$. We then study identifiability under embeddings: we establish relations between maximal identifiability, embeddability and graph dimension when network topologies are model as DAGs. Our results suggest the design of networks over $N$ nodes with maximal identifiability $Ω(\log N)$ using $O(\log N)$ monitors and a heuristic to boost maximal identifiability on a given network by simulating $d$-dimensional grids. We provide positive evidence of this heuristic through data extracted by exact computation of maximal identifiability on examples of small real networks.

cs.DS↗

arXiv2019

Vertex-Connectivity Measures for Node Failure Identification in Boolean Network Tomography

In this paper we study the node failure identification problem in undirected graphs by means of Boolean Network Tomography. We argue that vertex connectivity plays a central role. We show tight bounds on the maximal identifiability in a particular class of graphs, the Line of Sight networks. We prove slightly weaker bounds on arbitrary networks. Finally we initiate the study of maximal identifiability in random networks. We focus on two models: the classical Erdős-Rényi model, and that of Random Regular graphs. The framework proposed in the paper allows a probabilistic analysis of the identifiability in random networks giving a tradeoff between the number of monitors to place and the maximal identifiability.

cs.NI↗

arXiv2015

Inverse Galois Problem and Significant Methods

The inverse problem of Galois Theory was developed in the early 1800 s as an approach to understand polynomials and their roots. The inverse Galois problem states whether any finite group can be realized as a Galois group over Q (field of rational numbers). There has been considerable progress in this as yet unsolved problem. Here, we shall discuss some of the most significant results on this problem. This paper also presents a nice variety of significant methods in connection with the problem such as the Hilbert irreducibility theorem, Noether s problem, and rigidity method and so on.

math.HO↗