Point visibility graph recognition is NP-hard
نویسنده
چکیده
Given a 3-SAT formula, a graph can be constructed in polynomial time such that the graph is a point visibility graph if and only if the 3-SAT formula is satisfiable. This reduction establishes that the problem of recognition of point visibility graphs is NP-hard.
منابع مشابه
Partitions of planar point sets into polygons
In this paper, we characterize planar point sets that can be partitioned into disjoint polygons of arbitrarily specified sizes. We provide an algorithm to construct such a partition, if it exists, in polynomial time. We show that this problem is equivalent to finding a specified 2-factor in the visibility graph of the point set. The characterization for the case where all cycles have length 3 a...
متن کاملVisibility Graphs of Staircase Polygons and the Weak Bruhat Order, I: from Visibility Graphs to Maximal Chains
The recognition problem for visibility graphs of simple polygons is not known to be in NP, nor is it known to be NP-hard. It is, however, known to be in PSPACE. Further, every such visibility graph can be dismantled as a sequence of visibility graphs of convex fans. Any nondegenerate configuration of n points can be associated with a maximal chain in the weak Bruhat order of the symmetric group...
متن کاملRecognition and Complexity of Point Visibility Graphs
A point visibility graph is a graph induced by a set of points in the plane, where every vertex corresponds to a point, and two vertices are adjacent whenever the two corresponding points are visible from each other, that is, the open segment between them does not contain any other point of the set. We study the recognition problem for point visibility graphs: given a simple undirected graph, d...
متن کاملObstructing Visibilities with One Obstacle
Obstacle representations of graphs have been investigated quite intensely over the last few years. We focus on graphs that can be represented by a single obstacle. Given a (topologically open) polygon C and a finite set P of points in general position in the complement of C, the visibility graph GC(P ) has a vertex for each point in P and an edge pq for any two points p and q in P that can see ...
متن کاملA Time Dependent Pollution Routing Problem in Multi-graph
This paper considers a time dependent(the travel time is not constant throughout the day) pollution routing problem (TDPRP), which aids the decision makers in minimizing travel time, toll cost and emitted pollution cost. In complexity of urban areas most of the time one point is accessible from another with more than one edge. In contrast to previous TDPRP models, which are designed with only ...
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:
- Int. J. Comput. Geometry Appl.
دوره 26 شماره
صفحات -
تاریخ انتشار 2016