Related papers: Efficient Maximum Fair Clique Search over Large Ne…
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…
We consider problems of finding a maximum size/weight $t$-matching without forbidden subgraphs in an undirected graph $G$ with the maximum degree bounded by $t+1$, where $t$ is an integer greater than $2$. Depending on the variant forbidden…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in…
We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…
A variety of tasks on dynamic graphs, including anomaly detection, community detection, compression, and graph understanding, have been formulated as problems of identifying constituent (near) bi-cliques (i.e., complete bipartite graphs).…
In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for…
Given an edge-colored graph, the goal of the proportional fair matching problem is to find a maximum weight matching while ensuring proportional representation (with respect to the number of edges) of each color. The colors may correspond…
Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of…
Dense subgraph discovery (DSD) is a key graph mining primitive with myriad applications including finding densely connected communities which are diverse in their vertex composition. In such a context, it is desirable to extract a dense…
The rise of graph representation learning as the primary solution for many different network science tasks led to a surge of interest in the fairness of this family of methods. Link prediction, in particular, has a substantial social…
We consider a variant of the densest subgraph problem in networks with single or multiple edge attributes. For example, in a social network, the edge attributes may describe the type of relationship between users, such as friends, family,…
We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer),…
Graph federated learning enables the collaborative extraction of high-order information from distributed subgraphs while preserving the privacy of raw data. However, graph data often exhibits overlap among different clients. Previous…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Finding large "cliquish" subgraphs is a central topic in graph mining and community detection. A popular clique relaxation are 2-clubs: instead of asking for subgraphs of diameter one (these are cliques), one asks for subgraphs of diameter…
Finding dense subgraphs in a graph is a fundamental graph mining task, with applications in several fields. Algorithms for identifying dense subgraphs are used in biology, in finance, in spam detection, etc. Standard formulations of this…
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…
The Cluster Deletion problem takes a graph $G$ as input and asks for a minimum size set of edges $X$ such that $G-X$ is the disjoint union of complete graphs. An equivalent formulation is the Clique Partition problem, which asks to find a…