Related papers: A recognition algorithm for adjusted interval digr…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. Based on the position of the vertex in one of the graphs, it is determined the…
We present compact distributed interactive proofs for the recognition of two important graph classes, well-studied in the context of centralized algorithms, namely complement reducible graphs and distance-hereditary graphs. Complement…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a…
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. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our…
We consider the problem of constructing a bipartite graph whose degrees lie in prescribed intervals. Necessary and sufficient conditions for the existence of such graphs are well-known. However, existing realization algorithms suffer from…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing…
The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a…
Multiple interval graphs are a well-known generalization of interval graphs introduced in the 1970s to deal with situations arising naturally in scheduling and allocation. A $d$-interval is the union of $d$ intervals on the real line, and a…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
Minimal separators in graphs are an important concept in algorithmic graph theory. In particular, many problems that are NP-hard for general graphs are known to become polynomial-time solvable for classes of graphs with a polynomially…
An interval graph is proper iff it has a representation in which no interval contains another. Fred Roberts characterized the proper interval graphs as those containing no induced star $K_{1,3}$. Proskurowski and Telle have studied…
Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M…
We give a randomized algorithm that finds a minimum cut in an undirected weighted $m$-edge $n$-vertex graph $G$ with high probability in $O(m \log^2 n)$ time. This is the first improvement to Karger's celebrated $O(m \log^3 n)$ time…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
The graph classification problem has been widely studied; however, achieving an interpretable model with high predictive performance remains a challenging issue. This paper proposes an interpretable classification algorithm for attributed…