Greedy Nature Research Articles

A noniterative greedy algorithm for multiframe point correspondence

This paper presents a framework for finding point correspondences in monocular image sequences over multiple frames. The general problem of multiframe point correspondence is NP-hard for three or more frames. A polynomial time algorithm for a restriction of this problem is presented and is used as the basis of the proposed greedy algorithm for the general problem. The greedy nature of the proposed algorithm allows it to be used in real-time systems for tracking and surveillance, etc. In addition, the proposed algorithm deals with the problems of occlusion, missed detections, and false positives by using a single noniterative greedy optimization scheme and, hence, reduces the complexity of the overall algorithm as compared to most existing approaches where multiple heuristics are used for the same purpose. While most greedy algorithms for point tracking do not allow for entry and exit of the points from the scene, this is not a limitation for the proposed algorithm. Experiments with real and synthetic data over a wide range of scenarios and system parameters are presented to validate the claims about the performance of the proposed algorithm.

Induction of decision trees via evolutionary programming.

Decision trees have been used extensively in cheminformatics for modeling various biochemical endpoints including receptor-ligand binding, ADME properties, environmental impact, and toxicity. The traditional approach to inducing decision trees based upon a given training set of data involves recursive partitioning which selects partitioning variables and their values in a greedy manner to optimize a given measure of purity. This methodology has numerous benefits including classifier interpretability and the capability of modeling nonlinear relationships. The greedy nature of induction, however, may fail to elucidate underlying relationships between the data and endpoints. Using evolutionary programming, decision trees are induced which are significantly more accurate than trees induced by recursive partitioning. Furthermore, when assessed on previously unseen data in a 10-fold cross-validated manner, evolutionary programming induced trees exhibit a significantly higher accuracy on previously unseen data. This methodology is compared to single-tree and multiple-tree recursive partitioning in two domains (aerobic biodegradability and hepatotoxicity) and shown to produce less complex classifiers with average increases in predictive accuracy of 5-10% over the traditional method.

Efficient greedy learning of gaussian mixture models.

This article concerns the greedy learning of gaussian mixtures. In the greedy approach, mixture components are inserted into the mixture one after the other. We propose a heuristic for searching for the optimal component to insert. In a randomized manner, a set of candidate new components is generated. For each of these candidates, we find the locally optimal new component and insert it into the existing mixture. The resulting algorithm resolves the sensitivity to initialization of state-of-the-art methods, like expectation maximization, and has running time linear in the number of data points and quadratic in the (final) number of mixture components. Due to its greedy nature, the algorithm can be particularly useful when the optimal number of mixture components is unknown. Experimental results comparing the proposed algorithm to other methods on density estimation and texture segmentation are provided.

A Microchoice Bound for Continuous-Space Classification Algorithms

Classifiers are often constructed iteratively by introducing changes sequentially to an initial classifier. Langford and Blum (COLT'99: Proceedings of the 12th Annual Conference on Computational Learning Theory, 1999, San Mateo, CA: Morgan Kaufmann, pp. 209–214) take advantage of this structure (the microchoice structure), to obtain bounds for the generalization ability of such algorithms. These bounds can be sharper than more general bounds. This paper extends the applicability of the microchoice approach to the more realistic case where the classifier space is continuous and the sequence of changes is not restricted to a pre-fixed finite set. Proving the microchoice bound in the continuous case relies on a conditioning technique that is often used in proving VC results. It is shown how this technique can be used to convert any learning algorithm over a continuous space into a family of algorithms over discrete spaces. The new continuous microchoice result is applied to obtain a bound for the generalization ability of the perceptron algorithm. The greedy nature of the perceptron algorithm, which generates new classifiers by introducing corrections based on misclassified points, is exploited to obtain a generalization bound that has an asymptotic form of O( $$1/\sqrt n$$ ), where n is the training set size.

T-coffee: a novel method for fast and accurate multiple sequence alignment

We describe a new method (T-Coffee) for multiple sequence alignment that provides a dramatic improvement in accuracy with a modest sacrifice in speed as compared to the most commonly used alternatives. The method is broadly based on the popular progressive approach to multiple alignment but avoids the most serious pitfalls caused by the greedy nature of this algorithm. With T-Coffee we pre-process a data set of all pair-wise alignments between the sequences. This provides us with a library of alignment information that can be used to guide the progressive alignment. Intermediate alignments are then based not only on the sequences to be aligned next but also on how all of the sequences align with each other. This alignment information can be derived from heterogeneous sources such as a mixture of alignment programs and/or structure superposition. Here, we illustrate the power of the approach by using a combination of local and global pair-wise alignments to generate the library. The resulting alignments are significantly more reliable, as determined by comparison with a set of 141 test cases, than any of the popular alternatives that we tried. The improvement, especially clear with the more difficult test cases, is always visible, regardless of the phylogenetic spread of the sequences in the tests.

Evaluation of greedy, myopic and less-greedy heuristics for the single machine, total tardiness problem

Simple, yet highly effective modifications to the net benefit of relocation (NBR) heuristic of Holsenback and Russell provide significant improvements in solution quality without any increase in computational effort by tempering the greedy nature of the original NBR heuristic. Two lemmas reduce the size of the search while adhering to optimality conditions. Experimentation compares the modified NBR heuristic (M-NBR) with the two leading heuristics of the literature. Testing on 25, 50 and 100-job problems over a wide range of due dates and tardiness factors shows the M-NBR algorithm to be the best single-pass heuristic to date. We show that a composite heuristic, employing the better of the M-NBR and another leading heuristic solution, consistently produces near-optimal solutions with negligible CPU requirements.

The strong chromatic index of a cubic graph is at most 10

It is proved that a graph with maximum degree at most 3 has a strong edge-colouring with at most 10 colours. A simple algorithm achieving a strong edge-colouring with at most 10 colours for any graph with maximum degree at most 3 is described; the algorithm is of a greedy nature and has running time linear in the number of vertices of the graph.

Optimal parallel construction of prescribed tournaments

A tournament is a digraph in which every pair of vertices is connected by exactly one arc. The score list of a tournament is the sorted list of the out-degrees of its vertices. Given a nondecreasing sequence of nonnegative integers, is it the score list of some tournament? There is a simple test for answering this question. There is also a simple sequential algorithm for constructing a tournament with a given score list. However, this algorithm has a greedy nature, and seems hard to parallelize. We present a simple parallel algorithm for the construction problem. Our algorithm runs in time O(log n) and uses O( n 2/ log n) processors on a CREW PRAM, where n is the number of vertices. Since the size of the output is Θ( n 2), our algorithm achieves optimal speedup. The tournament constructed has the property that it is the closest possible to a transitive tournament in a precise sense.