相关论文: Labeling Schemes with Queries

The L(2, 1)-labeling of a digraph G is a function f from the node set of $G$ to the set of all nonnegative integers such that $|f(x)-f(y)| \geq 2$ if $x$ and $y$ are at distance 1, and $f(x)=f(y)$ if $x$ and $y$ are at distance 2, where the…

Semi-supervised learning has received attention from researchers, as it allows one to exploit the structure of unlabeled data to achieve competitive classification results with much fewer labels than supervised approaches. The Local and…

An {\em ancestry labeling scheme} labels the nodes of any tree in such a way that ancestry queries between any two nodes in a tree can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of…

A labeling scheme for nearest common ancestors assigns a distinct binary string, called the label, to every node of a tree, so that given the labels of two nodes (and no further information about the topology of the tree) we can compute the…

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…

Although multi-label learning can deal with many problems with label ambiguity, it does not fit some real applications well where the overall distribution of the importance of the labels matters. This paper proposes a novel learning…

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $p$ and size $q$. For $k\ge 1$, a bijection $f: V(G)\cup E(G) \to \{k, k+1, k+2, \ldots, k+p+q-1\}$ such that $f(uv)= |f(u) - f(v)|$ for every edge $uv\in E(G)$ is said…

Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a…

Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling $f \colon V (G) \rightarrow A$ of the vertices of some graph $G$ induces an edge…

Do higher-order network structures aid graph semi-supervised learning? Given a graph and a few labeled vertices, labeling the remaining vertices is a high-impact problem with applications in several tasks, such as recommender systems, fraud…

In this paper, we answer the question of when inserting label noise (less informative labels) can instead return us more accurate and fair models. We are primarily inspired by three observations: 1) In contrast to reducing label noise…

Laplace learning is a popular machine learning algorithm for finding missing labels from a small number of labelled feature vectors using the geometry of a graph. More precisely, Laplace learning is based on minimising a graph-Dirichlet…

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…

In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…

Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…

Let $G$ a bipartite graph with vertex bipartition $\{A,B\}$ and let $m=|E(G)|$. An $(A,B)$-uniformly ordered labeling of $G$ is a labeling $f\colon V\rightarrow [0,2m]$ which, among other conditions, requires that there exists $\lambda\in…

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is…

We develop a formalism to address statistical pattern recognition of graph valued data. Of particular interest is the case of all graphs having the same number of uniquely labeled vertices. When the vertex labels are latent, such graphs are…

An antimagic labeling for a graph $G$ with $m$ edges is a bijection $f: E(G) \to \{1, 2, \dots, m\}$ so that $\phi_f(u) \neq \phi_f(v)$ holds for any pair of distinct vertices $u, v \in V(G)$, where $\phi_f(x) = \sum_{x \in e} f(e)$. A…

Node classification on graphs often requires labeled nodes, yet obtaining labels at graph scale is expensive. When node attributes contain semantic content, such as paper abstracts, web pages, or product descriptions, large language models…