Multi-Instance Multi-Label learning (MIML) deals with data objects that are represented by a bag of instances and associated with a set of class labels simultaneously. Previous studies typically assume that for every training example, all positive labels are tagged whereas the untagged labels are all negative. In many real applications such as image annotation, however, the learning problem oft...

A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices with the same label contains a vertex with a larger label. The rank number of a graph is the fewest number of labels that can be used in a ranking. The rank number of a graph is known for many families, including the ladder graph P2 × Pn. We consider how ”bending” a ladder affects ...

In this paper, we obtain closed formulas for the number of reachable vertices in labelled plane trees by paths lengths, sinks, leaf first children, left most path, non-first and non-leaves. Our counting objects are having their edges oriented from a vertex lower label towards higher label. For each statistic, average vertices. Moreover, formula on $n$ such that exactly $k\leq n$ root.

With the recent advances in graph neural networks, there is a rising number of studies on graph-based multi-label classification with consideration object dependencies within visual data. Nevertheless, representations can become indistinguishable due to complex nature label relationships. We propose image framework based transformer networks fully exploit inter-label interactions. The paper pre...

The automatic text categorization and the medical diagnosis were the first domain of applications that requires Multi-label classification. It consists to assign more than one label for each object. Later, its applications were widely increased to cover additional fields like functional genomics, music, biology, scene, video etc... There are two main categories of approaches for Multi-label cla...

Path Layout is a fundamental graph problem in label switching protocols. This problem is raised in various protocols such as the traditional ATM protocol and MPLS which is a new label switching protocol standardized recently by the IETF. Path layout is essentially the problem of reducing the size of the label-table in a router. The size is equivalent to the number of different paths that pass t...

A square difference 3-equitable labeling of a graph G with vertex set V is a bijection f from V to {1, 2,.... | V | } jg such that if each edge uv is assigned the label -1 if |[f (u)]2 [f (v)]2 | = -1(mod 4), the label 0 if |[f (u)]2 [f (v)]2 | = 0(mod 4) and the label 1 if |[f (u)]2 [f (v)]| = 1(mod 4), then the number of edges labeled with i and the number of edges labelled with j differ by a...

This paper presents computational studies for the traveling salesman problem with time windows by applying a bi-directional resource-bounded label correcting algorithm. Label extensions and dominance start simultaneously in both forward and backward directions: the forward direction from the starting depot and the backward direction from the terminating depot. The resultant label extension proc...