Related papers: Fast Algorithms for the Maximum Clique Problem on …
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection graphs of paths on an orthogonal grid. The class $B_k$-EPG is the subclass of EPG graphs where the path on the grid associated to each vertex has at most $k$ bends.…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…
Cohesive subgraph mining on attributed graphs is a fundamental problem in graph data analysis. Existing cohesive subgraph mining algorithms on attributed graphs do not consider the fairness of attributes in the subgraph. In this paper, we,…
Natural Language Processing (NLP) provides highly effective tools for interpreting and handling human language, offering a broad spectrum of applications. In this paper, we address a classic combinatorial problem -- finding graph partitions…
In the well known planted clique problem, a clique (or alternatively, an independent set) of size $k$ is planted at random in an Erdos-Renyi random $G(n, p)$ graph, and the goal is to design an algorithm that finds the maximum clique (or…
Recently Chase determined the maximum possible number of cliques of size $t$ in a graph on $n$ vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the version of this question in which we ask that the graph…
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…
We tackle the problem of counting the number of $k$-cliques in large-scale graphs, for any constant $k \ge 3$. Clique counting is essential in a variety of applications, among which social network analysis. Due to its computationally…
Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the…
We study the complexity of Maximum Clique in intersection graphs of convex objects in the plane. On the algorithmic side, we extend the polynomial-time algorithm for unit disks [Clark '90, Raghavan and Spinrad '03] to translates of any…
We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete.
Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…
NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp's 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
The advent of new special-purpose hardware such as FPGA or ASIC-based annealers and quantum processors has shown potential in solving certain families of complex combinatorial optimization problems more efficiently than conventional CPUs.…
Mining dense quasi-cliques is a well-known clustering task with applications ranging from social networks over collaboration graphs to document analysis. Recent work has extended this task to multiple graphs; i.e. the goal is to find groups…