Scheduling advertisements on a web page to maximize revenue
Many web sites (e.g. Hotmail, Yahoo) provide free services to the users while generating revenues from advertising. Advertising revenue is, therefore, critical for these sites. This in turn raises the question, how should advertisements at a web site be scheduled in a planning horizon to maximize revenue. Advertisements on the web are specified by geometry and display frequency and both of these factors need to be considered in developing a solution to the advertisement scheduling problem. Since this problem belongs to the class of NP-hard problems, we first develop a heuristic called LSMF to solve the problem. This heuristic is then combined with a genetic algorithm (GA) to develop a hybrid GA. The hybrid GA solution is first compared with the upper bound obtained by running CPLEX for the integer programming formulation of the problem. It is then also compared with an existing algorithm proposed in the literature. Our computational results show that the hybrid GA performs exceptionally well in the sense that it provides optimal or near optimal solution for a wide range of problem instances of realistic sizes and the improvements over existing algorithm are substantial. Finally we present a case study to illustrate how revenue could be significantly increased with a small improvement in the advertisement schedule. It is the first such study in this setup.

title: Scheduling Web Advertisements: A Note on the Minspace Problem
abstract: Free services to internet users are commonly available on many web sites e.g., Hotmail and Yahoo. For such sites, revenue generated from advertisements (hereafter also called “ads”) placed on the web pages is critical for survival. An effective way to schedule ads on web pages to optimize certain performance measures is an important problem that these sites need to address.In this note, we report improved approximation algorithms for the following problem: ads from a set of n ads A = {Ai,...,An} are to be placed on a web page during a planning horizon that is divided into N time intervals. In each time interval, ads are shown in a rectangular space called a slot. An ad Ai is specified by its size si and frequency wi and is to be scheduled in exactly wi slots. We are required to find a schedule that minimizes the maximum fullness among all the slots, where the fullness of a slot is the sum of the sizes of ads scheduled in that slot. Our results include (i) the first online algorithm with a performance bound of $$2 - \frac{1}{N}$$, and (ii) two offline algorithms with performance guarantees of $$1 + 1\frac{1}{\sqrt{2}}$$ and $$\frac{3}{2}$$, respectively. These bounds are significant improvements over those for previously known algorithms presented in Adler, Gibbons, and Matias (2002) and Dawande, Kumar, and Sriskandarajah (2003).

title: Hierarchical Fusion of Multiple Classifiers for Hyperspectral Data Analysis
abstract: Many classification problems involve high dimensional inputs and a large number of classes. Multiclassifier fusion approaches to such difficult problems typically centre around smart feature extraction, input resampling methods, or input space partitioning to exploit modular learning. In this paper, we investigate how partitioning of the output space (i.e. the set of class labels) can be exploited in a multiclassifier fusion framework to simplify such problems and to yield better solutions. Specifically, we introduce a hierarchical technique to recursively decompose a C-class problem into C_1 ) class problems. A generalised modular learning framework is used to partition a set of classes into two disjoint groups called meta-classes. The coupled problems of finding a good partition and of searching for a linear feature extractor that best discriminates the resulting two meta-classes are solved simultaneously at each stage of the recursive algorithm. This results in a binary tree whose leaf nodes represent the original C classes. The proposed hierarchical multiclassifier framework is particularly effective for difficult classification problems involving a moderately large number of classes. The proposed method is illustrated on a problem related to classification of landcover using hyperspectral data: a 12-class AVIRIS subset with 180 bands. For this problem, the classification accuracies obtained were superior to most other techniques developed for hyperspectral classification. Moreover, the class hierarchies that were automatically discovered conformed very well with human domain experts’ opinions, which demonstrates the potential of using such a modular learning approach for discovering domain knowledge automatically from data.

title: Asynchronous Genetic Algorithms for Heterogeneous Networks Using Coarse-Grained Dataflow
abstract: Genetic algorithms (GAs) are an attractive class of techniques for solving a variety of complex search and optimization problems. Their implementation on a distributed platform can provide the necessary computing power to address large-scale problems of practical importance. On heterogeneous networks, however, the performance of a global parallel GA can be limited by synchronization points during the computation, particularly those between generations. We present a new approach for implementing asynchronous GAs based on the dataflow model of computation -- an approach that retains the functional properties of a global parallel GA. Experiments conducted with an air quality optimization problem and others show that the performance of GAs can be substantially improved through dataflow-based asynchrony.

title: Bounding blocking probabilities and throughput in queueing networks with buffer capacity constraints
abstract: We propose a new technique for upper and lower bounding of the throughput and blocking probabilities in queueing networks with buffer capacity constraints, i.e., some buffers in the network have finite capacity. By studying the evolution of multinomials of the state of the system in its assumed steady state, we obtain constraints on the possible behavior of the system. Using these constraints, we obtain linear programs whose values upper and lower bound the performance measures of interest, namely throughputs or blocking probabilities. The main advantages of this new technique are that the computational complexity does not increase with the size of the finite buffers and that the technique is applicable to systems in which some buffers have infinite capacity. The technique is demonstrated on examples taken from both manufacturing systems and communication networks. As a special case, for the M/M/s/s queue, we establish the asymptotic exactness of the bounds, i.e., that the bounds on the blocking probability asymptotically approach the exact value as the degree of the multinomials considered is increased to infinity.

title: A Hierarchical Multiclassifier System for Hyperspectral Data Analysis
abstract: Many real world classification problems involve high dimensional inputs and a large number of classes. Feature extraction and modular learning approaches can be used to simplify such problems. In this paper, we introduce a hierarchical multiclassifier paradigm in which a C- class problem is recursively decomposed into C - 1 two-class problems. A generalized modular learning framework is used to partition a set of classes into two disjoint groups called meta-classes. The coupled problem of finding a good partition and of searching for a linear feature extractor that best discriminates the resulting two meta-classes are solved simultaneously at each stage of the recursive algorithm. This results in a binary tree whose leaf nodes represent the original C classes. The proposed hierarchical multiclassifier architecture was used to classify 12 types of landcover from 183-dimensional hyperspectral data. The classification accuracy was significantly improved by 4 to 10% relative to other feature extraction and modular learning approaches. Moreover, the class hierarchy that was automatically discovered conformed very well with a human domain expert's opinion, which demonstrates the potential of such a modular learning approach for discovering domain knowledge automatically from data.

title: Discriminative random fields: a discriminative framework for contextual interaction in classification
abstract: In this work we present discriminative random fields (DRFs), a discriminative framework for the classification of image regions by incorporating neighborhood interactions in the labels as well as the observed data. The discriminative random fields offer several advantages over the conventional Markov random field (MRF) framework. First, the DRFs allow to relax the strong assumption of conditional independence of the observed data generally used in the MRF framework for tractability. This assumption is too restrictive for a large number of applications in vision. Second, the DRFs derive their classification power by exploiting the probabilistic discriminative models instead of the generative models used in the MRF framework. Finally, all the parameters in the DRF model are estimated simultaneously from the training data unlike the MRF framework where likelihood parameters are usually learned separately from the field parameters. We illustrate the advantages of the DRFs over the MRF framework in an application of man-made structure detection in natural images taken from the Corel database.