Related papers: Making Bidirected Graphs Strongly Connected
We state the graph-theoretic computational problem of finding tight paths in a directed, edge-weighted graph, as well as its simplification of finding tight pairs. These problems are motivated by the need of algorithms that find so-called…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
This paper is the first from a series of papers that establish a common analogue of the strong component and basilica decompositions for bidirected graphs. A bidirected graph is a graph in which a sign $+$ or $-$ is assigned to each end of…
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…
A weighted coloured-edge graph is a graph for which each edge is assigned both a positive weight and a discrete colour, and can be used to model transportation and computer networks in which there are multiple transportation modes. In such…
This paper studies the problem of proper-walk connection number: given an undirected connected graph, our aim is to colour its edges with as few colours as possible so that there exists a properly coloured walk between every pair of…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
In order to study real-world systems, many applied works model them through signed graphs, i.e. graphs whose edges are labeled as either positive or negative. Such a graph is considered as structurally balanced when it can be partitioned…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
We show how to find and efficiently maintain maximal k-edge-connected subgraphs in undirected graphs. In particular, we provide the following results. (1) A general framework for maintaining the maximal k-edge-connected subgraphs upon…
In this paper, we prove two lower bounds for the maximum matching size in an arbitrary undirected graph. Despite their simplicity, these results are not widely known. This article aims to bring pleasure to the reader by giving short…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Clustering bipartite graphs is a fundamental task in network analysis. In the high-dimensional regime where the number of rows $n_1$ and the number of columns $n_2$ of the associated adjacency matrix are of different order, existing methods…