The Straight-Line RAC Drawing Problem Is NP-Hard

نویسندگان

  • Evmorfia N. Argyriou
  • Michael A. Bekos
  • Antonios Symvonis
چکیده

Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the study of RAC drawings, in which every pair of crossing edges intersects at right angle. In this work, we demonstrate a class of graphs with unique RAC combinatorial embedding and we employ members of this class in order to show that it is NP-hard to decide whether a graph admits a straight-line RAC drawing. Date: September 27, 2010.

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

On the Perspectives Opened by Right Angle Crossing Drawings

Right Angle Crossing (RAC) drawings are polyline drawings where each crossing forms four right angles. RAC drawings have been introduced because cognitive experiments provided evidence that increasing the number of crossings does not decrease the readability of a drawing if edges cross at right angles. We investigate to what extent RAC drawings can help in overcoming the limitations of widely a...

متن کامل

Moving Vertices to Make Drawings Plane

In John Tantalo’s on-line game Planarity the player is given a non-plane straight-line drawing of a planar graph. The aim is to make the drawing plane as quickly as possible by moving vertices. In this paper we investigate the related problem MinMovedVertices which asks for the minimum number of vertex moves. First, we show that MinMovedVertices is NP-hard and hard to approximate. Second, we es...

متن کامل

On Upward Drawings of Trees on a Given Grid

Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algo...

متن کامل

One Sided Crossing Minimization Is NP-Hard for Sparse Graphs

The one sided crossing minimization problem consists of placing the vertices of one part of a bipartite graph on prescribed positions on a straight line and finding the positions of the vertices of the second part on a parallel line and drawing the edges as straight lines such that the number of pairwise edge crossings is minimized. This problem represents the basic building block used for draw...

متن کامل

The Complexity of Drawing Graphs on Few Lines and Few Planes

It is well known that any graph admits a crossing-free straight-line drawing in R3 and that any planar graph admits the same even in R2. For a graph G and d ∈ {2, 3}, let ρd(G) denote the minimum number of lines in Rd that together can cover all edges of a drawing of G. For d = 2, G must be planar. We investigate the complexity of computing these parameters and obtain the following hardness and...

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:
  • J. Graph Algorithms Appl.

دوره 16  شماره 

صفحات  -

تاریخ انتشار 2011