Showing papers on "Greedy algorithm published in 2003"

Optimal structure identification with greedy search

Abstract: In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.

Computationally efficient bandwidth allocation and power control for OFDMA

Abstract: The paper studies the problem of finding an optimal subcarrier and power allocation strategy for downlink communication to multiple users in an orthogonal-frequency-division multiplexing-based wireless system. The problem of minimizing total power consumption with constraints on bit-error rate and transmission rate for users requiring different classes of service is formulated and simple algorithms with good performance are derived. The problem of joint allocation is divided into two steps. In the first step, the number of subcarriers that each user gets is determined based on the users' average signal-to-noise ratio. The algorithm is shown to find the distribution of subcarriers that minimizes the total power required when every user experiences a flat-fading channel. In the second stage of the algorithm, it finds the best assignment of subcarriers to users. Two different approaches are presented, the rate-craving greedy algorithm and the amplitude-craving greedy algorithm. A single cell with one base station and many mobile stations is considered. Numerical results demonstrate that the proposed low complexity algorithms offer comparable performance with an existing iterative algorithm.

Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP

Abstract: In this article, we will formalize the method of dual fitting and the idea of factor-revealing LP. This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem. Their approximation factors are 1.861 and 1.61, with running times of O(m log m) and O(n3), respectively, where n is the total number of vertices and m is the number of edges in the underlying complete bipartite graph between cities and facilities. The algorithms are used to improve recent results for several variants of the problem.

Efficient greedy learning of Gaussian mixture models

Abstract: 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.

An Efficient Genetic Algorithm for the p -Median Problem

Abstract: We propose a new genetic algorithm for a well-known facility location problem. The algorithm is relatively simple and it generates good solutions quickly. Evolution is facilitated by a greedy heuristic. Computational tests with a total of 80 problems from four different sources with 100 to 1,000 nodes indicate that the best solution generated by the algorithm is within 0.1% of the optimum for 85% of the problems. The coding effort and the computational effort required are minimal, making the algorithm a good choice for practical applications requiring quick solutions, or for upper-bound generation to speed up optimal algorithms.

How asymmetry helps load balancing

Abstract: This article deals with randomized allocation processes placing sequentially n balls into n bins. We consider multiple-choice algorithms that choose d locations (bins) for each ball at random, inspect the content of these locations, and then place the ball into one of them, for example, in a location with minimum number of balls. The goal is to achieve a good load balancing. This objective is measured in terms of the maximum load, that is, the maximum number of balls in the same bin.Multiple-choice algorithms have been studied extensively in the past. Previous analyses typically assume that the d locations for each ball are drawn uniformly and independently from the set of all bins. We investigate whether a nonuniform or dependent selection of the d locations of a ball may lead to a better load balancing. Three types of selection, resulting in three classes of algorithms, are distinguished: (1) uniform and independent, (2) nonuniform and independent, and (3) nonuniform and dependent.Our first result shows that the well-studied uniform greedy algorithm (class 1) does not obtain the smallest possible maximum load. In particular, we introduce a nonuniform algorithm (class 2) that obtains a better load balancing. Surprisingly, this algorithm uses an unfair tie-breaking mechanism, called Always-Go-Left, resulting in an asymmetric assignment of the balls to the bins. Our second result is a lower bound showing that a dependent allocation (class 3) cannot yield significant further improvement.Our upper and lower bounds on the maximum load are tight up to additive constants, proving that the Always-Go-Left algorithm achieves an almost optimal load balancing among all sequential multiple-choice algorithm. Furthermore, we show that the results for the Always-Go-Left algorithm can be generalized to allocation processes with more balls than bins and even to infinite processes in which balls are inserted and deleted by an oblivious adversary.

Efficiently solving general weapon-target assignment problem by genetic algorithms with greedy eugenics

Abstract: A general weapon-target assignment (WTA) problem is to find a proper assignment of weapons to targets with the objective of minimizing the expected damage of own-force asset. Genetic algorithms (GAs) are widely used for solving complicated optimization problems, such as WTA problems. In this paper, a novel GA with greedy eugenics is proposed. Eugenics is a process of improving the quality of offspring. The proposed algorithm is to enhance the performance of GAs by introducing a greedy reformation scheme so as to have locally optimal offspring. This algorithm is successfully applied to general WTA problems. From our simulations for those tested problems, the proposed algorithm has the best performance when compared to other existing search algorithms.

Guided Local Search for the Three-Dimensional Bin-Packing Problem

Abstract: The three-dimensional bin-packing problem is the problem of orthogonally packing a set of boxes into a minimum number of three-dimensional bins. In this paper we present a heuristic algorithm based on guided local search. Starting with an upper bound on the number of bins obtained by a greedy heuristic, the presented algorithm iteratively decreases the number of bins, each time searching for a feasible packing of the boxes. The process terminates when a given time limit has been reached or the upper bound matches a precomputed lower bound. The algorithm can also be applied to two-dimensional bin-packing problems by having a constant depth for all boxes and bins. Computational experiments are reported for two- and three-dimensional instances with up to 200 boxes, showing that the algorithm on average finds better solutions than do heuristics from the literature.

Sequential greedy approximation for certain convex optimization problems

Abstract: A greedy algorithm for a class of convex optimization problems is presented. The algorithm is motivated from function approximation using a sparse combination of basis functions as well as some of its variants. We derive a bound on the rate of approximate minimization for this algorithm, and present examples of its application. Our analysis generalizes a number of earlier studies.

Finding optimal models for small gene networks.

Abstract: Finding gene networks from microarray data has been one focus of research in recent years. Given search spaces of super-exponential size, researchers have been applying heuristic approaches like greedy algorithms or simulated annealing to infer such networks. However, the accuracy of heuristics is uncertain, which--in combination with the high measurement noise of microarrays--makes it very difficult to draw conclusions from networks estimated by heuristics. We present a method that finds optimal Bayesian networks of considerable size and show first results of the application to yeast data. Having removed the uncertainty due to the heuristic methods, it becomes possible to evaluate the power of different statistical models to find biologically accurate networks.

Measuring the similarity of labeled graphs

Abstract: This paper proposes a similarity measure to compare cases represented by labeled graphs. We first define an expressive model of directed labeled graph, allowing multiple labels on vertices and edges. Then we define the similarity problem as the search of a best mapping, where a mapping is a correspondence between vertices of the graphs. A key point of our approach is that this mapping does not have to be univalent, so that a vertex in a graph may be associated with several vertices of the other graph. Another key point is that the quality of the mapping is determined by generic functions, which can be tuned in order to implement domain-dependant knowledge. We discuss some computational issues related to this problem, and we describe a greedy algorithm for it. Finally, we show that our approach provides not only a quantitative measure of the similarity, but also qualitative information which can prove valuable in the adaptation phase of CBR.

UniqueProt: Creating representative protein sequence sets.

Abstract: UniqueProt is a practical and easy to use web service designed to create representative, unbiased data sets of protein sequences. The largest possible representative sets are found through a simple greedy algorithm using the HSSP-value to establish sequence similarity. UniqueProt is not a real clustering program in the sense that the ‘representatives’ are not at the centres of well-defined clusters since the definition of such clusters is problem-specific. Overall, UniqueProt is a reasonable fast solution for bias in data sets. The service is accessible at http://cubic.bioc.columbia.edu/services/uniqueprot; a command-line version for Linux is downloadable from this web site.

On the existence of almost greedy bases in Banach spaces

Abstract: We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X has a basis and contains a complemented subspace with a symmetric basis and finite cotype then X has an almost greedy basis. We show that c0 is the only L∞ space to have a quasi-greedy basis. The Banach spaces which contain almost greedy basic sequences are characterized.

A non-iterative greedy algorithm for multi-frame point correspondence

Abstract: We present 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 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 points from the scene, this is not a limitation for the proposed algorithm. Experiments with real and synthetic data show that the proposed algorithm outperforms the existing techniques and is applicable in more general settings.

A study of greedy, local search, and ant colony optimization approaches for car sequencing problems

Abstract: This paper describes and compares several heuristic approaches for the car sequencing problem. We first study greedy heuristics, and show that dynamic ones clearly outperform their static counterparts. We then describe local search and ant colony optimization (ACO) approaches, that both integrate greedy heuristics, and experimentally compare them on benchmark instances. ACO yields the best solution quality for smaller time limits, and it is comparable to local search for larger limits. Our best algorithms proved one instance being feasible, for which it was formerly unknown whether it is satisfiable or not.

Publish/Subscribe Tree Construction in Wireless Ad-Hoc Networks

Abstract: Wireless ad-hoc publish/subscribe systems combine a publish/subscribe mechanism with wireless ad-hoc networking. The combination, although very attractive, has not been studied extensively in the literature. This paper addresses an important problem of such systems: how to construct an optimal publish/ subscribe tree for routing information from the source to all interested recipients. First we precisely define the optimality of a publish/subscribe tree by developing a metric to evaluate its "efficiency." The optimality metric takes into account both the goal of a publish/subscribe system (i.e., to route a set of events), and the characteristics of an ad-hoc network (for example, devices are resource limited). We propose a greedy algorithm, SHOPPARENT, which builds the publish/ subscribe tree in a fully distributed fashion. A key feature is that this algorithm can be "subscription-aware", allowing it to use publication/subscription information in order to find a better outcome. Our simulations show that SHOPPARENT's performance is within 15% of optimal under normal configurations. We also study the effect of geographically localized subscriptions.

The facility location problem with general cost functions

Abstract: In this paper, we introduce a generalized version of the facility location problem in which the facility cost is a function of the number of clients assigned to the facility. We focus on the case of concave facility cost functions. We observe that this problem can be reduced to the uncapacitated facility location problem. We analyze a natural greedy algorithm for this problem and show that its approximation factor is at most 1.861. We also consider several generalizations and variants of this problem. © 2003 Wiley Periodicals, Inc.

Greedy heuristics and an evolutionary algorithm for the bounded-diameter minimum spanning tree problem

Abstract: Given a connected, weighted, undirected graph G and a bound D, the bounded-diameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NP-hard for 4

News from the online traveling repairman

Abstract: In the traveling repairman problem (TRP), a tour must be found through every one of a set of points (cities) in some metric space such that the weighted sum of completion times of the cities is minimized. Given a tour, the completion time of a city is the time traveled on the tour before the city is reached. In the online traveling repairman problem OLTRP requests for visits to cities arrive online while the repairman is traveling. We analyze the performance of algorithms for the online problem using competitive analysis, where the cost of an online algorithm is compared to that of an optimal offline algorithm. Feuerstein and Stougie [8] present a 9-competitive algorithm for the OlTrp on the real line. In this paper we show how to use techniques from online-scheduling to obtain a 6-competitive deterministic algorithm for the OlTrp on any metric space. We also present a randomized algorithm with competitive ratio of 3/ln 2 2.1282 for the L-OLDARP on the line, 4e-5/2e-3 > 2.41041 for the L-OLDARP on general metric spaces, 2 for the OLTRP on the line, and 7/3 for the OLTRP on general metric spaces.

Approximation algorithms for the test cover problem

Abstract: In the test cover problem a set of m items is given together with a collection of subsets, called tests. A smallest subcollection of tests is to be selected such that for each pair of items there is a test in the selection that contains exactly one of the two items. It is known that the problem is NP-hard and that the greedy algorithm has a performance ratio O(log m). We observe that, unless P=NP, no polynomial-time algorithm can do essentially better. For the case that each test contains at most k items, we give an O(log k)-approximation algorithm. We pay special attention to the case that each test contains at most two items. A strong relation with a problem of packing paths in a graph is established, which implies that even this special case is NP-hard. We prove APX-hardness of both problems, derive performance guarantees for greedy algorithms, and discuss the performance of a series of local improvement heuristics.

An Adaptive Greedy Algorithm for Solving Large RBF Collocation Problems

Abstract: The solution of operator equations with radial basis functions by collocation in scattered points leads to large linear systems which often are nonsparse and ill-conditioned But one can try to use only a subset of the data for the actual collocation, leaving the rest of the data points for error checking This amounts to finding “sparse” approximate solutions of general linear systems arising from collocation This contribution proposes an adaptive greedy method with proven (but slow) linear convergence to the full solution of the collocation equations The collocation matrix need not be stored, and the progress of the method can be controlled by a variety of parameters Some numerical examples are given

Optimizing exact genetic linkage computations

Abstract: Genetic linkage analysis is a challenging application which requires Bayesian networks consisting of thousands of vertices. Consequently, computing the likelihood of data, which is needed for learning linkage parameters, using exact inference procedures calls for an extremely efficient implementation that carefully optimizes the order of conditioning and summation operations. In this paper we present the use of stochastic greedy algorithms for optimizing this order. Our algorithm has been incorporated into the newest version of superlink, which is currently the fastest genetic linkage program for exact likelihood computations in general pedigrees. We demonstrate an order of magnitude improvement in run times of likelihood computations using our new optimization algorithm, and hence enlarge the class of problems that can be handled effectively by exact computations.

Million city traveling salesman problem solution by divide and conquer clustering with adaptive resonance neural networks

Abstract: The Traveling Salesman Problem (TSP) is a very hard optimization problem in the field of operations research. It has been shown to be NP-complete, and is an often-used benchmark for new optimization techniques. One of the main challenges with this problem is that standard, non-AI heuristic approaches such as the Lin-Kernighan algorithm (LK) and the chained LK variant are currently very effective and in wide use for the common fully connected, Euclidean variant that is considered here. This paper presents an algorithm that uses adaptive resonance theory (ART) in combination with a variation of the Lin-Kernighan local optimization algorithm to solve very large instances of the TSP. The primary advantage of this algorithm over traditional LK and chained-LK approaches is the increased scalability and parallelism allowed by the divide-and-conquer clustering paradigm. Tours obtained by the algorithm are lower quality, but scaling is much better and there is a high potential for increasing performance using parallel hardware.

Pareto-optimization-based run-time task scheduling for embedded systems

Abstract: Pareto-set-based optimization can be found in several different areas of embedded system design. One example is task scheduling, where different task mapping and ordering choices for a target platform will lead to different performance/cost tradeoffs. To explore this design space at run-time, a fast and effective heuristic is needed. We have modeled the problem as the well known Multiple Choice Knapsack Problem(MCKP) and have developed a fast greedy heuristic for the run-time task scheduling. To show the effectiveness of our algorithm, examples from randomly generated task graphs and realistic applications are studied. Compared to the optimal dynamic programming solver, the heuristic is more than ten times faster while the result is less than 5\% away from the optimum. Moreover, due to its iterative feature, the algorithm is well suitable to be used as an on-line algorithm.