Related papers: Computational complexity of distance edge labeling
For both triangulations of point sets and simple polygons, it is known that determining the flip distance between two triangulations is an NP-hard problem. To gain more insight into flips of triangulations and to characterize "where edges…
A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…
A distance labeling scheme labels the $n$ nodes of a graph with binary strings such that, given the labels of any two nodes, one can determine the distance in the graph between the two nodes by looking only at the labels. A $D$-preserving…
Semantic boundary and edge detection aims at simultaneously detecting object edge pixels in images and assigning class labels to them. Systematic training of predictors for this task requires the labeling of edges in images which is a…
Multi-label classification is a type of supervised learning where an instance may belong to multiple labels simultaneously. Predicting each label independently has been criticized for not exploiting any correlation between labels. In this…
We give bounds on the L(2,1)-labeling number of a simple graph in terms of its order and its maximum degree. We also describe an infinite class of graphs of which the elements have the highest L(2,1)-labeling numbers in terms of their…
In the Boundary Labeling problem, we are given a set of $n$ points, referred to as sites, inside an axis-parallel rectangle $R$, and a set of $n$ pairwise disjoint rectangular labels that are attached to $R$ from the outside. The task is to…
The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new…
The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…
Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…
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…
A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…
A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. We consider the cartographic problem to place non-overlapping road labels along…
$k$-Approximate distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the $k$-approximation of the distance between any two vertices $u$ and $v$ can be determined efficiently by merely…
An L(2,1)-labeling of a graph $G$ is an assignment $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $x$ and $y$ are adjacent and $|f(x)-f(y)|\ge 1$ if $x$ and $y$ are at distance 2, for all…
A good edge-labelling of a simple, finite graph is a labelling of its edges with real numbers such that, for every ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. In this paper we prove that any graph on…
Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via crossing-free leaders. We…
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…
We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of…
For positive integers $j\ge k$, an $L(j,k)$-labeling of a digraph $D$ is a function $f$ from $V(D)$ into the set of nonnegative integers such that $|f(x)-f(y)|\ge j$ if $x$ is adjacent to $y$ in $D$ and $|f(x)-f(y)|\ge k$ if $x$ is of…