Related papers: Combinatorial algorithm for counting small induced…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
With recent advances in high-throughput cell biology the amount of cellular biological data has grown drastically. Such data is often modeled as graphs (also called networks) and studying them can lead to new insights into molecule-level…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes' input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do…
Complex networks are relational data sets commonly represented as graphs. The analysis of their intricate structure is relevant to many areas of science and commerce, and data sets may reach sizes that require distributed storage and…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
To solve many problems on graphs, graph traversals are used, the usual variants of which are the depth-first search and the breadth-first search. Implementing a graph traversal we consequently reach all vertices of the graph that belong to…
Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph -- in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs.…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…