Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance geometry approach for special graph coloring problems   One of the most important combinatorial optimization problems is graph
coloring. There are several variations of this problem involving additional
constraints either on vertices or edges. They constitute models for real
applications, such as channel assignment in mobile wireless networks. In this
work, we consider some coloring problems involving distance constraints as
weighted edges, modeling them as distance geometry problems. Thus, the vertices
of the graph are considered as embedded on the real line and the coloring is
treated as an assignment of positive integers to the vertices, while the
distances correspond to line segments, where the goal is to find a feasible
intersection of them. We formulate different such coloring problems and show
feasibility conditions for some problems. We also propose implicit enumeration
methods for some of the optimization problems based on branch-and-prune methods
proposed for distance geometry problems in the literature. An empirical
analysis was undertaken, considering equality and inequality constraints,
uniform and arbitrary set of distances, and the performance of each variant of
the method considering the handling and propagation of the set of distances
involved.

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int