منابع مشابه
Unit disk graph recognition is NP-hard
Unit disk graphs are the intersection graphs of unit diameter closed disks in the plane. This paper reduces SATISFIABILITY to the problem of recognizing unit disk graphs. Equivalently, it shows that determining if a graph has sphericity 2 or less, even if the graph is planar or is known to have sphericity at most 3, is NP-hard. We show how this reduction can be extended to 3 dimensions, thereby...
متن کاملPoint visibility graph recognition is NP-hard
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.
متن کاملMinimum Bisection Is NP-hard on Unit Disk Graphs
In this paper we prove that the Min-Bisection problem is NP-hard on unit disk graphs, thus solving a longstanding open question.
متن کاملNearest Neighbour Graph Realizability is NP-hard
1 I n t r o d u c t i o n This paper investigates the problem of realizing a given graph G as a "nearest neighbour graph" of a set P of points in the plane. Roughly speaking, a "nearest neighbour graph" is a geometric graph formed from a set of points in the plane by joining two points if one is the nearest neighbour of the other. Fig. 1. A mutual nearest neighbour graph One specific kind of ne...
متن کاملMetric Dimension for Gabriel Unit Disk Graphs Is NP-Complete
We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NPcomplete even if the networks are unit disk graphs that contain only Gabriel edges. This problem is equivalent to Metric Dimension for Gabriel unit disk graphs. The Gabriel edges of a unit disc graph induce a planar O( √ n) distance and an optimal ener...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Geometry
سال: 1998
ISSN: 0925-7721
DOI: 10.1016/s0925-7721(97)00014-x