On Extending a Partial Straight-Line Drawing

نویسنده

  • Maurizio Patrignani
چکیده

In this paper we investigate the computational complexity of the following problem. Given a planar graph in which some vertices have already been placed in the plane (i.e., a partial embedding), place the remaining vertices to form a planar straight-line drawing of the graph. We show that the above extensibility problem, mentioned in the 2003 paper “Selected Open Problems in Graph Drawing” [1], is NP-complete.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Note on Minimum-Segment Drawings of Planar Graphs

A straight-line drawing of a planar graph G is a planar drawing of G, where each vertex is mapped to a point on the Euclidean plane and each edge is drawn as a straight line segment. A segment in a straight-line drawing is a maximal set of edges that form a straight line segment. A minimum-segment drawing of G is a straightline drawing of G, where the number of segments is the minimum among all...

متن کامل

The Complexity of Drawing a Graph in a Polygonal Region

We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal region, with some vertices of the graph assigned to points on the boundary of the region, place the remaining vertices to create a planar straight-line drawing of the graph inside the region. This strengthens an NP-hardness result by Patrignani on extending partial plana...

متن کامل

Canonical Orders and Schnyder Realizers

Every planar graph has a crossings-free drawing in the plane. Formally, a straight-line drawing of a planar graph G is one where each vertex is placed at a point in the plane and each edge is represented by a straight-line segment between the two corresponding points such that no two edges cross each other, except possibly at their common endpoints. A straight-line grid drawing of G is a straig...

متن کامل

3D Graph Drawing with Simulated Annealing

A recent trend in graph drawing is directed to the visualiza-tion of graphs in 3D 1, 5, 6]. A promising research direction concerns the extension of proven 2D techniques to 3D. We present a system extending the simulated annealing algorithm of Davidson and Harel 2] for straight-line two-dimensional drawings of general undirected graphs to three dimensions. This system features an advanced 3D us...

متن کامل

Outerplanar Graph Drawings with Few Slopes

We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions. We prove that ∆ − 1 edge slopes suffice for every outerplanar graph with maximum degree ∆ > 4. This improves on the previous bound of O(∆), which was shown for planar partial 3-trees,...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Int. J. Found. Comput. Sci.

دوره 17  شماره 

صفحات  -

تاریخ انتشار 2005