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Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case.…
In a graph A, for each two arbitrary vertices g, h with d(g,h)=2,|MAg2h|=mAg2h is introduced the number of edges of A that are closer to g than to h. We say A is a 2-edge distance-balanced graph if we have mAg2h=mAh2g. In this article, we…
We investigate the parameterized complexity of the recognition problem for the proper $H$-graphs. The $H$-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph $H$, and the properness means that the…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
We introduce a novel architecture for graph networks which is equivariant to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes. In particular, it is equivariant to the Euclidean and…
Nowadays, the analysis of complex phenomena modeled by graphs plays a crucial role in many real-world application domains where decisions can have a strong societal impact. However, numerous studies and papers have recently revealed that…
The maximum matching width is a width-parameter that is defined on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the…
Clique-width is a well-studied graph parameter. For graphs of bounded clique-width, many problems that are NP-hard in general can be polynomial-time solvable. The fact motivates several studies to investigate whether the clique-width of…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…
We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Mim-width and sim-width are among the most powerful graph width parameters, with sim-width more powerful than mim-width, which is in turn more powerful than clique-width. While several $\mathsf{NP}$-hard graph problems become tractable for…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
We present a near-linear-time algorithm that, given a bridgeless cubic graph, finds a perfect matching intersecting every 3-edge-cut in exactly one edge. This improves over a cubic algorithm of Boyd et al. for the same problem, and over our…
Graph data is ubiquitous in academia and industry, from social networks to bioinformatics. The pervasiveness of graphs today has raised the demand for algorithms that can answer various questions: Which products would a user like to…
Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in…