Complexity of Some Geometric Problems
نویسنده
چکیده
We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on the rectilinear crossing number and intersection graphs of line segments, we argue that there is a need to recognize this level of complexity as its own class.
منابع مشابه
Parameterized Complexity of Geometric Problems
This paper surveys parameterized complexity results for NP-hard geometric problems. Geometric problems arise frequently in application domains as diverse as computer graphics [19], computer vision [4, 35, 43], VLSI design [64], geographic information systems [73, 30], graph drawing [72], and robotics [65, 37], and typically involve (sets of) geometric objects, such as, points, line segments, ba...
متن کاملSimplicity v/s Complexity in the Framework of Geometric Asymptotic Analysis and Some New Applications of the Concentration Phenomenon
We introduce a concept of Simplicity which in a sense corresponds to the reverse direction to the concept of Complexity. Many problems of Asymptotic Geometric Analysis rotate around this notion. We also describe the concept of Concentration and suggest a new direction of possible applications of the Concentration Phenomenon.
متن کاملField Study and Evaluation of Buckling Behavior of Cylindrical Steel Tanks with Geometric Imperfections under Uniform External Pressure
Construction and assembling process of shell structures has caused main problems. In these structures, there is no possibility for the integrated construction due to their large shell extent and they are built using a number of welded curved panel parts; hence, some geometrical imperfections emerge. Most of these imperfections are caused by the process of welding, transportation, inappropriate ...
متن کاملInverse Identification of Circular Cavity in a 2D Object via Boundary Temperature Measurements Using Artificial Neural Network
In geometric inverse problems, it is assumed that some parts of domain boundaries are not accessible and geometric shape and dimensions of these parts cannot be measured directly. The aim of inverse geometry problems is to approximate the unknown boundary shape by conducting some experimental measurements on accessible surfaces. In the present paper, the artificial neural network is used to sol...
متن کاملGeometric Complexity Theory II: Towards Explicit Obstructions for Embeddings among Class Varieties
In [26], henceforth referred to as Part I, we suggested an approach to the P vs. NP and related lower bound problems in complexity theory through geometric invariant theory. In particular, it reduces the arithmetic (characteristic zero) version of the NP 6⊆ P conjecture to the problem of showing that a variety associated with the complexity class NP cannot be embedded in a variety associated wi...
متن کاملOn the Complexity of Some Geometric Problems in Unbounded Dimension
This paper examines the complexity of several geometric problems due to un bounded dimension The problems considered are i minimum cover of points by unit cubes ii minimum cover of points by unit balls and iii minimum number of lines to hit a set of balls Each of these problems is proven not to have a poly nomial approximation scheme unless P NP Speci c lower bounds on the error ratios attainab...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010