Related papers: Neighbourhood Evaluation Criteria for Vertex Cover…
Community detection is one of the most studied problems on complex networks. Although hundreds of methods have been proposed so far, there is still no universally accepted formal definition of what is a good community. As a consequence, the…
A prototypical graph problem is centered around a graph-theoretic property for a set of vertices and a solution to it is a set of vertices for which the desired property holds. The task is to decide whether, in the given graph, there exists…
We introduce a simple, efficient and precise polynomial heuristic for a key NP complete problem, minimum vertex cover. Our method is iterative and operates in probability space. Once a stable probability solution is found we find the true…
The problem of nearest-neighbor (NN) condensation aims to reduce the size of a training set of a nearest-neighbor classifier while maintaining its classification accuracy. Although many condensation techniques have been proposed, few bounds…
Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…
In the context of the chromatic-number problem, a critical graph is an instance where the deletion of any element would decrease the graph's chromatic number. Such instances have shown to be interesting objects of study for deepen the…
Learning from many real-world datasets is limited by a problem called the class imbalance problem. A dataset is imbalanced when one class (the majority class) has significantly more samples than the other class (the minority class). Such…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership…
The algorithmic differentiation (AD) of mathematical functions can be interpreted as a sequence of vertex eliminations in an underlying directed acyclic graph. The problem of determining a minimum-cost elimination ordering, which we call…
Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
A community detection algorithm is considered to have a resolution limit if the scale of the smallest modules that can be resolved depends on the size of the analyzed subnetwork. The resolution limit is known to prevent some community…
Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors…
When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop…
Vertex Cover parameterized by the solution size k is the quintessential fixed-parameter tractable problem. FPT algorithms are most interesting when the parameter is small. Several lower bounds on k are well-known, such as the maximum size…
We consider the (precedence constrained) Minimum Feedback Arc Set problem with triangle inequalities on the weights, which finds important applications in problems of ranking with inconsistent information. We present a surprising structural…
This paper considers the problem of algorithm selection for community detection. The aim of community detection is to identify sets of nodes in a network which are more interconnected relative to their connectivity to the rest of the…
We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge…
Given a set of vertices in a network, that we believe are of interest for the application under analysis, community search is the problem of producing a subgraph potentially explaining the relationships existing among the vertices of…