Complexity of Planar Embeddability of Trees inside Simple Polygons
نویسندگان
چکیده
Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane bounded by a simple polygon and a free tree, we show that deciding whether there is a planar straight-line embedding of the tree on the point set inside the simple polygon is NP-complete. This implies that the straight-line constrained point-set embedding of trees is also NP-complete, which was posed as an open problem in [8].
منابع مشابه
A New Heuristic Algorithm for Drawing Binary Trees within Arbitrary Polygons Based on Center of Gravity
Graphs have enormous usage in software engineering, network and electrical engineering. In fact graphs drawing is a geometrically representation of information. Among graphs, trees are concentrated because of their ability in hierarchical extension as well as processing VLSI circuit. Many algorithms have been proposed for drawing binary trees within polygons. However these algorithms generate b...
متن کاملDrawing Free Trees Inside Simple Polygons Using Polygon Skeleton
Most of graph drawing algorithms draw graphs on unbounded planes. In this paper we introduce a new polyline grid drawing algorithm for drawing free trees on plane regions which are bounded by simple polygons. Our algorithm uses the simulated annealing (SA) method, and by means of the straight skeletons of the bounding polygons guides the SA method to uniformly distribute the vertices of the giv...
متن کاملSingle-Point Visibility Constraint Minimum Link Paths in Simple Polygons
We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...
متن کاملProportional Contact Representations of Planar Graphs Technical Report CS 2011 - 11
We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by a point-contact or a side-contact between the corresponding polygons. Specifically, we consider proportional contact representations, where given vertex weights are represented by the areas of the corresponding polygons. Several natural optimization goals for such repr...
متن کاملLinear - Time Algorithms for Proportional Contact Graph Representations ?
In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/0908.4041 شماره
صفحات -
تاریخ انتشار 2009