Exodic Matching in Geometrical Probability
نویسنده
چکیده
Given n uniformly and independently distributed points in a ball of unit volume in dimension d, it is well established that the length of several combinatorial optimization problems (including the minimum spanning tree (MST), the minimum matching (M), the traveling salesman problem (TSP), etc.) on these n points obeys laws of large numbers. It has been a long open conjecture that a central limit theorem holds for the length of these problems. In this paper we establish the first central limit theorem in this class of problems for the length of the tree and matching produced by a natural heuristic (the exodic heuristic) for the MST and the minimum matching problem respectively. Moreover, we make precise analytical estimates for the variance of the length that the heuristic produces and verify them experimentally.
منابع مشابه
An Asymptotic Determination of the Minimum Spanning Tree and Minimum Matching Constants in Geometrical Probability
Given n uniformly and independently distributed points in a ball of unit volume in dimension d, it is well established that the length of several combinatorial optimization problems (including the minimum spanning tree (MST), the minimum matching (M), the traveling salesman problem (TSP), etc.) on these n points is asymptotic to P(d) n(d-1)/d, where the constant B(d) depends on the dimension d ...
متن کاملImage alignment via kernelized feature learning
Machine learning is an application of artificial intelligence that is able to automatically learn and improve from experience without being explicitly programmed. The primary assumption for most of the machine learning algorithms is that the training set (source domain) and the test set (target domain) follow from the same probability distribution. However, in most of the real-world application...
متن کاملAutomatic Feature Based Image Registration using DWT and SIFT
Image Processing Technology provides opportunities for search of related or similar images. We proposed an approach to identify some visual objects or "Landmarks" in an image and generate relevant images in matching probability order using “IMAGE REGISTRATION” Methods. Image registration is an important and fundamental task in image processing used to match two different images. Given two or mo...
متن کاملKnowledge-based Image Analysis for 3d Edge Extraction and Road Reconstruction
Road network extraction from aerial images has received attention in photogrammetry and computer vision for decades. We present a concept for road network reconstruction from aerial images using knowledge-based image analysis. In contrast to other approaches, the proposed approach uses multiple cues about the object existence, employs existing knowledge, rules and models, and treats each road s...
متن کاملGeometrical Optics Approach to Markov-Modulated Fluid Models
We analyze asymptotically a differential-difference equation, that arises in a Markovmodulated fluid model. Here there are N identical sources that turn on and off, and when on they generate fluid at unit rate into a buffer, which process the fluid at a rate c < N. In the steady state limit, the joint probability distribution of the buffer content and the number of active sources satisfies a sy...
متن کامل