DeepAI AI Chat
Log In Sign Up

Geometric Embedding of Path and Cycle Graphs in Pseudo-convex Polygons

by   Hamid Hoorfar, et al.

Given a graph G with n vertices and a set S of n points in the plane, a point-set embedding of G on S is a planar drawing such that each vertex of G is mapped to a distinct point of S . A straight-line point-set embedding is a point-set embedding with no edge bends or curves. The point-set embeddability problem is NP-complete, even when G is 2 -connected and 2 -outerplanar. It has been solved polynomially only for a few classes of planar graphs. Suppose that S is the set of vertices of a simple polygon. A straight-line polygon embedding of a graph is a straight-line point-set embedding of the graph onto the vertices of the polygon with no crossing between edges of graph and the edges of polygon. In this paper, we present O(n) -time algorithms for polygon embedding of path and cycle graphs in simple convex polygon and same time algorithms for polygon embedding of path and cycle graphs in a large type of simple polygons where n is the number of vertices of the polygon.


page 1

page 2

page 3

page 4


Fan-Crossing Free Graphs

A graph is fan-crossing free if it admits a drawing in the plane so that...

Crossing Minimization in Perturbed Drawings

Due to data compression or low resolution, nearby vertices and edges of ...

Nearest-Neighbor Decompositions of Drawings

Let 𝒟 be a set of straight-line segments in the plane, potentially cross...

Casting graph isomorphism as a point set registration problem using a simplex embedding and sampling

Graph isomorphism is an important problem as its worst-case time complex...

Retracting Graphs to Cycles

We initiate the algorithmic study of retracting a graph into a cycle in ...

A genetic algorithm for straight-line embedding of a cycle onto a given set of points inside simple polygons

In this paper, we have examined the problem of embedding a cycle of n ve...

Embedding into Special Classes of Cyclic Graphs and its Applications in VLSI Layout

Graph embedding is the major technique which is used to map guest graph ...