Related papers: A Practical Maximum Clique Algorithm for Matching …
The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or…
Robust estimation is essential in correspondence-based Point Cloud Registration (PCR). Existing methods using maximal clique search in compatibility graphs achieve high recall but suffer from exponential time complexity, limiting their use…
Clique is one of the most fundamental models for cohesive subgraph mining in network analysis. Existing clique model mainly focuses on unsigned networks. However, in real world, many applications are modeled as signed networks with positive…
This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled…
This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. The manuscript covers in a simple way…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it…
The maximum clique (MC) problem is a challenging graph mining problem which, due to its NP-hard nature, can take a substantial amount of execution time. The MC problem is dominated by set intersection operations similar to Maximal Clique…
3D point cloud registration is a fundamental problem in computer vision and robotics. There has been extensive research in this area, but existing methods meet great challenges in situations with a large proportion of outliers and time…
The Clique Problem has a reduction to the Maximum Flow Network Interdiction Problem. We review the reduction to evolve a polynomial time algorithm for the Clique Problem. A computer program in C language has been written to validate the…
Estimating the rigid transformation between two LiDAR scans through putative 3D correspondences is a typical point cloud registration paradigm. Current 3D feature matching approaches commonly lead to numerous outlier correspondences, making…
Critical to the registration of point clouds is the establishment of a set of accurate correspondences between points in 3D space. The correspondence problem is generally addressed by the design of discriminative 3D local descriptors on the…
Mining cohesive subgraphs in attributed graphs is an essential problem in the domain of graph data analysis. The integration of fairness considerations significantly fuels interest in models and algorithms for mining fairness-aware cohesive…
We analyze the problem of determining whether 2 given point clouds in 2D, with any distinct cardinality and any number of outliers, have subsets of the same size that can be matched via a rigid motion. This problem is important, for…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security, etc. Most existing MCE algorithms focus…
In this paper we modify an algorithm for updating a maximal clique enumeration after an edge insertion to provide an algorithm that runs in linear time with respect to the number of cliques containing one of the edge's endpoints, whereas…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…
A $k$-clique is a dense graph, consisting of $k$ fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint…