Related papers: Shorter Labeling Schemes for Planar Graphs
This manuscript introduces Diophantine labeling, a new way of labeling of the vertices for finite simple undirected graphs with some divisibility condition on the edges. Maximal graphs admitting Diophantine labeling are investigated and…
A coprime labeling of a simple graph of order $n$ is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used can be taken to be the first $n$ positive integers. In this paper, we…
We consider graph labelings with an assignment of odd prime numbers to the vertices. Similarly to graceful graphs, a labeling is said to be elegant if the absolute differences between the labels of adjacent vertices describe exactly the…
Hub labeling schemes are popular methods for computing distances on road networks and other large complex networks, often answering to a query within a few microseconds for graphs with millions of edges. In this work, we study their…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…
A \emph{graceful labeling} of a graph $G$ is an injective function $f : V(G) \to \{0, \ldots, |E(G)|\}$ such that $\{\,|f(u)-f(v)| : uv \in E(G)\,\} = \{1, \ldots, |E(G)|\}$. If such a labeling exists, then we call $G$ \emph{graceful}.…
For an arbitrary finite family of graphs, the distance labeling problem asks to assign labels to all nodes of every graph in the family in a way that allows one to recover the distance between any two nodes of any graph from their labels.…
We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property pi is called a pi-graph. If pi satisfies certain properties, then an n-node m-edge pi-graph G can…
This paper investigates the problem of active learning for binary label prediction on a graph. We introduce a simple and label-efficient algorithm called S2 for this task. At each step, S2 selects the vertex to be labeled based on the…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
Node classification on graphs is an important research problem with many applications. Real-world graph data sets may not be balanced and accurate as assumed by most existing works. A challenging setting is positive-unlabeled (PU) node…
A scalable semi-supervised node classification method on graph-structured data, called GraphHop, is proposed in this work. The graph contains attributes of all nodes but labels of a few nodes. The classical label propagation (LP) method and…
A good edge-labelling of a simple graph is a labelling of its edges with real numbers such that, for any ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. Say a graph is good if it admits a good…
Graph Neural Networks (GNNs) have shown state-of-the-art improvements in node classification tasks on graphs. While these improvements have been largely demonstrated in a multi-class classification scenario, a more general and realistic…
In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in…
Graph neural networks (GNNs) learn to represent nodes by aggregating information from their neighbors. As GNNs increase in depth, their receptive field grows exponentially, leading to high memory costs. Several existing methods address this…
Weakly-supervised segmentation with label-efficient sparse annotations has attracted increasing research attention to reduce the cost of laborious pixel-wise labeling process, while the pairwise affinity modeling techniques play an…
Graph neural networks (GNNs) achieve remarkable success in graph-based semi-supervised node classification, leveraging the information from neighboring nodes to improve the representation learning of target node. The success of GNNs at node…
Given a set of nonempty subsets of some universal set, their intersection graph is defined as the graph with one vertex for each set and two vertices are adjacent precisely when their representing sets have non-empty intersection. Sometimes…
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures,…