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Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…

Simple graph algorithms such as PageRank have been the target of numerous hardware accelerators. Yet, there also exist much more complex graph mining algorithms for problems such as clustering or maximal clique listing. These algorithms are…

A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is…

A popular paradigm for 3D point cloud registration is by extracting 3D keypoint correspondences, then estimating the registration function from the correspondences using a robust algorithm. However, many existing 3D keypoint techniques tend…

Combinatorial optimization (CO) problems are pivotal across various industrial applications, where the speed of solving these problems is crucial. Improving the performance of CO solvers across diverse input instances requires fine-tuning…

The maximum clique problem (MCP) is to find the largest complete subgraph in an undirected graph, that is, the subgraph in which there are edges between every two different vertices. It is an NP-Hard problem with wide applications,…

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…

We investigate a number of recently reported exact algorithms for the maximum clique problem (MCQ, MCR, MCS, BBMC). The program code used is presented and critiqued showing how small changes in implementation can have a drastic effect on…

The Maximum Common Subgraph (MCS) problem plays a crucial role across various domains, bridging theoretical exploration and practical applications in fields like bioinformatics and social network analysis. Despite its wide applicability,…

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…

Finding maximum cliques in large networks is a challenging combinatorial problem with many real-world applications. We present a fast algorithm to achieve the exact solution for the maximum clique problem in large sparse networks based on…

We conjecture that the worst case number of experiments necessary and sufficient to discover a causal graph uniquely given its observational Markov equivalence class can be specified as a function of the largest clique in the Markov…

Given simple undirected graph G = (V, E), the Maximum Clique Problem(MCP) is that of finding a maximum-cardinality subset Q of V such that any two vertices in Q are adjacent. We present a modified local search algorithm for this problem.…

In this work, we present a constant-round algorithm for the $2$-ruling set problem in the Congested Clique model. As a direct consequence, we obtain a constant round algorithm in the MPC model with linear space-per-machine and optimal total…

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…

In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…

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…

We consider the problem of identifying a maximum clique in a given graph. We have proposed a mathematical model for this problem. The model resembles the matrix decomposition of the adjacency matrix of a given graph. The objective function…

Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…

We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation…