Acoplamientos óptimos de caminos de longitud dos

96 páginas. Maestría en Optimización.Let P be a set of 3k points in the Euclidean plane. A 3-matching is a partition of P into k subsets of 3 points each, called triplets. The cost of each triplet fa; b; cg is given by minfjabj + jbcj; jbcj + jcaj; jcaj + jabjg, and the cost of the 3-matching is the sum of the costs of its triplets. The Euclidean 3-matching problem consists on finding a minimum cost 3-matching of P under the Euclidean metric. In the usual formulation of the Euclidean 3- matching problem we need to find a minimum cost 3-matching of P. This problem has several applications, especially in the insertion of components on a printed circuit board. Johnsson, Magyar, and Nevalainen introduced two integer programming formulations for this problem, and proved that its decision version is NP-complete if each triplet has an arbitrary positive cost (i.e., not necessarily Euclidean). The problem remains NP-complete even if the points of P correspond to vertices of a unit distance graph (a metric cost function). In this work, we prove that the linear programming relaxations of these two models are equivalent. Then we introduce three new integer programming models that use fewer variables than those from Johnsson, Magyar, and Nevalainen. We also compare the linear programming relaxations of the models. Besides the minimization problem, we are also interested in a similar maximization problem: finding a maximum cost non-crossing Euclidean 3-matching of P, where non-crossing means that no two segments intersect in a common interior point. Both problems, minimum cost and maximum cost non-crossing, are challenging, and we believe that both are NP-hard. Exact solutions to both problems can be attained through integer programming; however, in order to obtain good solutions in feasible times, we fix our attention to heuristics. We present three heuristics specially designed for our problems and compare their solutions and execution times against solving the exact models

Path Planning for Cooperative Routing of Air-Ground Vehicles

We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles travel cooperatively satisfying the communication limits, and visit a set of targets. We present a mixed integer linear programming (MILP) formulation and develop a branch-and-cut algorithm to solve the path planning problem for the ground and air vehicles. The effectiveness of the proposed approach is corroborated through extensive computational experiments on several randomly generated instances

The pharmacophore kernel for virtual screening with support vector machines

We introduce a family of positive definite kernels specifically optimized for the manipulation of 3D structures of molecules with kernel methods. The kernels are based on the comparison of the three-points pharmacophores present in the 3D structures of molecul es, a set of molecular features known to be particularly relevant for virtual screening applications. We present a computationally demanding exact implementation of these kernels, as well as fast approximations related to the classical fingerprint-based approa ches. Experimental results suggest that this new approach outperforms state-of-the-art algorithms based on the 2D structure of mol ecules for the detection of inhibitors of several drug targets

Weakly-Supervised Alignment of Video With Text

Suppose that we are given a set of videos, along with natural language descriptions in the form of multiple sentences (e.g., manual annotations, movie scripts, sport summaries etc.), and that these sentences appear in the same temporal order as their visual counterparts. We propose in this paper a method for aligning the two modalities, i.e., automatically providing a time stamp for every sentence. Given vectorial features for both video and text, we propose to cast this task as a temporal assignment problem, with an implicit linear mapping between the two feature modalities. We formulate this problem as an integer quadratic program, and solve its continuous convex relaxation using an efficient conditional gradient algorithm. Several rounding procedures are proposed to construct the final integer solution. After demonstrating significant improvements over the state of the art on the related task of aligning video with symbolic labels [7], we evaluate our method on a challenging dataset of videos with associated textual descriptions [36], using both bag-of-words and continuous representations for text.Comment: ICCV 2015 - IEEE International Conference on Computer Vision, Dec 2015, Santiago, Chil

Information retrieval and mining in high dimensional databases

This dissertation is composed of two parts. In the first part, we present a framework for finding information (more precisely, active patterns) in three dimensional (3D) graphs. Each node in a graph is an undecoraposable or atomic unit and has a label. Edges are links between the atomic units. Patterns are rigid substructures that may occur in a graph after allowing for an arbitrary number of whole-structure rotations and translations as well as a small number (specified by the user) of edit operations in the patterns or in the graph. (When a pattern appears in a graph only after the graph has been modified, we call that appearance approximate occurrence. ) The edit operations include relabeling a node, deleting a node and inserting a node. The proposed method is based on the geometric hashing technique, which hashes node-triplets of the graphs into a 3D table and compresses the label-triplets in the table. To demonstrate the utility of our algorithms, we discuss two applications of them in scientific data mining. First, we apply the method to locating frequently occurring motifs in two families of proteins pertaining to RNA-directed DNA Polymerase and Thymidylate Synthase, and use the motifs to classify the proteins. Then we apply the method to clustering chemical compounds pertaining to aromatic, bicyclicalkanes and photosynthesis. Experimental results indicate the good performance of our algorithms and high recall and precision rates for both classification and clustering. We also extend our algorithms for processing a class of similarity queries in databases of 3D graphs. In the second part of the dissertation, we present an index structure, called MetricMap, that takes a set of objects and a distance metric and then maps those objects to a k-dimensional pseudo-Euclidean space in such a way that the distances among objects are approximately preserved. Our approach employs sampling and the calculation of eigenvalues and eigenvectors. The index structure is a useful tool for clustering and visualization in data intensive applications, because it replaces expensive distance calculations by sum-of-square calculations. This can make clustering in large databases with expensive distance metrics practical. We compare the index structure with another data mining index structure, FastMap, proposed by Faloutsos and Lin, according to two criteria: relative error and clustering accuracy. For relative error, we show that (i) FastMap gives a lower relative error than MetrieMap for Euclidean distances, (ii) MetricMap gives a lower relative error than Fast Map for non-Euclidean distances (i.e., general distance metrics), and (iii) combining the two reduces the error yet further. A similar result is obtained when comparing the accuracy of clustering. These results hold for different data sizes. The main qualitative conclusion is that these two index structures capture complenleiltary information about distance metrics and therefore can be used together to great benefit. The net effect is that multi-day computations can be done in minutes. We have implemented the proposed algorithms and the MetricMap index structure into a toolkit. This toolkit will be useful for data mining, visualization, and approximate retrieval in scientific, multimedia and high dimensional databases

Algorithmic and technical improvements: Optimal solutions to the (Generalized) Multi-Weber Problem

Rosing has recently demonstrated a new method for obtaining optimal solutions to the (Generalized) Multi-Weber Problem and proved the optimality of the results. The method develops all convex hulls and then covers the destinations with disjoint convex hulls. This paper seeks to improve implementation of the algorithm to make such solutions economically attractive. Four areas are considered: sharper decision rules to eliminate unnecessary searching, bit pattern matching as a method of recording a history and eliminating duplication, vector intrinsic functions to speed up comparisons, and profiling a program to maximize operating efficiency. Computational experience is also presented

Fast, Linear Time, m-Adic Hierarchical Clustering for Search and Retrieval using the Baire Metric, with linkages to Generalized Ultrametrics, Hashing, Formal Concept Analysis, and Precision of Data Measurement

We describe many vantage points on the Baire metric and its use in clustering data, or its use in preprocessing and structuring data in order to support search and retrieval operations. In some cases, we proceed directly to clusters and do not directly determine the distances. We show how a hierarchical clustering can be read directly from one pass through the data. We offer insights also on practical implications of precision of data measurement. As a mechanism for treating multidimensional data, including very high dimensional data, we use random projections.Comment: 17 pages, 45 citations, 2 figure

Multi-Image Semantic Matching by Mining Consistent Features

This work proposes a multi-image matching method to estimate semantic correspondences across multiple images. In contrast to the previous methods that optimize all pairwise correspondences, the proposed method identifies and matches only a sparse set of reliable features in the image collection. In this way, the proposed method is able to prune nonrepeatable features and also highly scalable to handle thousands of images. We additionally propose a low-rank constraint to ensure the geometric consistency of feature correspondences over the whole image collection. Besides the competitive performance on multi-graph matching and semantic flow benchmarks, we also demonstrate the applicability of the proposed method for reconstructing object-class models and discovering object-class landmarks from images without using any annotation.Comment: CVPR 201