16926436
Optimal Interdiction of Unreactive Markovian Evaders
The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction, the task of the interdictor is to find a set of edges in a weighted network such that the removal of those edges would maximally increase the cost to an evader of traveling on a path through the network. 
 
Our work is motivated by cases in which the evader has incomplete information about the network or lacks planning time or computational power, e.g. when authorities set up roadblocks to catch bank robbers, the criminals do not know all the roadblock locations or the best path to use for their escape. 
 
We introduce a model of network interdiction in which the motion of one or more evaders is described by Markov processes and the evaders are assumed not to react to interdiction decisions. The interdiction objective is to find an edge set of size B , that maximizes the probability of capturing the evaders. 
 
We prove that similar to the standard least-cost formulation for deterministic motion this interdiction problem is also NP-hard. But unlike that problem our interdiction problem is submodular and the optimal solution can be approximated within 1 *** 1/e using a greedy algorithm. Additionally, we exploit submodularity through a priority evaluation strategy that eliminates the linear complexity scaling in the number of network edges and speeds up the solution by orders of magnitude. Taken together the results bring closer the goal of finding realistic solutions to the interdiction problem on global-scale networks.
6961558
Minimizing a stochastic maximum-reliability path
We consider a stochastic network interdiction problem in which the goal is to detect an evader, who selects a maximum-reliability path. Subject to a resource constraint, the interdictor installs sensors on a subset of the network’s arcs to minimize the value of the evader’s maximum-reliability path, i.e., to maximize the detection probability. When this decision is made, the evader’s origin–destination pair is known to the interdictor only through a probability distribution. Our model is framed as a stochastic mixed-integer program and solved by an enhanced L-shaped decomposition method. Our primary enhancement is via a valid inequality, which we call a step inequality. In earlier work [Morton et al., IIE Trans 39 (2007), 3–14], we developed step inequalities for the special case in which the evader encounters at most one sensor on an origin–destination path. Here, we generalize the step inequality to the case where the evader encounters multiple sensors. In this more general setting, the step inequality is tightly coupled to the decomposition scheme. An efficient separation algorithm identifies violated step inequalities and strengthens the linear programming relaxation of the L-shaped method’s master program. We apply this solution procedure with further computational enhancements to a collection of test problems. © 2008 Wiley Periodicals, Inc. NETWORKS, Vol. 52(3), 111–119 2008
108674
Sample Selection for Maximal Diversity
The problem of selecting a sample subset sufficient to preserve diversity arises in many applications. One example is in the design of recombinant inbred lines (RIL) for genetic association studies. In this context, genetic diversity is measured by how many alleles are retained in the resulting inbred strains. RIL panels that are derived from more than two parental strains, such as the collaborative cross (Churchill et al., 2004), present a particular challenge with regard to which of the many existing lab mouse strains should be included in the initial breeding funnel in order to maximize allele retention. A similar problem occurs in the study of customer reviews when selecting a subset of products with a maximal diversity in reviews. Diversity in this case implies the presence of a set of products having both positive and negative ranks for each customer. In this paper, we demonstrate that selecting an optimal diversity subset is an NP-complete problem via reduction to set cover. This reduction is sufficiently tight that greedy approximations to the set cover problem directly apply to maximizing diversity. We then suggest a slightly modified subset selection problem in which an initial greedy diversity solution is used to effectively prune an exhaustive search for all diversity subsets bounded from below by a specified coverage threshold. Extensive experiments on real datasets are performed to demonstrate the effectiveness and efficiency of our approach.
44456878
A 2-Stage Partial Distortion Search Algorithm for Block Motion Estimation
In this paper, we propose a novel 2-Stage Partial Distortion Search (2S-PDS) algorithm to reduce the computational complexity in block motion estimation algorithms. In this algorithm, an early-rejection stage is introduced where the partial distortion of a decimated pixel block is calculated and compared with its local minimum. A block is rejected without calculating the full distortion of the entire block if the partial distortion is larger. In order to reduce the probability of false rejection, the local minimum is amplified by a pre-defined threshold before the comparison. Experimental results show that the proposed algorithm can reduce the complexity of block motion estimation algorithm significantly with only marginal performance penalty. The proposed algorithm can be used in combination with full-search or other fast search algorithms.
8030498
A novel joint rate control scheme for the coding of multiple real time video programs
The objective of joint rate control is to achieve a better and more uniform picture quality by exploiting the complexity of each program. In this paper, a novel joint rate control scheme is presented for real time coding of multiple video programs. In our scheme, the total available channel bandwidth is firstly assigned to each program in proportion to its information content. A novel control scheme, which is adaptive to the variation of distributed bandwidth, is then presented in our design to determine quantization parameters and the number of skipping frames for each program. As a result, the proposed scheme can be considered as a "look current" scheme, which outperforms many existing ones in terms of coding complexity and video quality.
14571890
COBBLER: combining column and row enumeration for closed pattern discovery
The problem of mining frequent closed patterns has received considerable attention recently as it promises to have much less redundancy compared to discovering all frequent patterns. Existing algorithms can presently be separated into two groups, feature (column) enumeration and row enumeration. Feature enumeration algorithms like CHARM and CLOSET+ are efficient for datasets with small number of features and large number of rows since the number of feature combinations to be enumerated is small. Row enumeration algorithms like CARPENTER on the other hand are more suitable for datasets (eg. bioinformatics data) with large number of features and small number of rows. Both groups of algorithms, however, will encounter problem for datasets that have large number of rows and features. In this paper, we describe a new algorithm called COBBLER which can efficiently mine such datasets . COBBLER is designed to dynamically switch between feature enumeration and row enumeration depending on the data characteristic in the process of mining. As such, each portion of the dataset can be processed using the most suitable method, making the mining more efficient. Several experiments on real-life and synthetic datasets show that COBBLER is an order of magnitude better than previous closed pattern mining algorithms like CHARM, CLOSET+ and CARPENTER.
2768791
Finding representative set from massive data
In the information age, data is pervasive. In some applications, data explosion is a significant phenomenon. The massive data volume poses challenges to both human users and computers. In this project, we propose a new model for identifying representative set from a large database. A representative set is a special subset of the original dataset, which has three main characteristics: It is significantly smaller in size compared to the original dataset. It captures the most information from the original dataset compared to other subsets of the same size. It has low redundancy among the representatives it contains. We use information-theoretic measures such as mutual information and relative entropy to measure the representativeness of the representative set. We first design a greedy algorithm and then present a heuristic algorithm that delivers much better performance. We run experiments on two real datasets and evaluate the effectiveness of our representative set in terms of coverage and accuracy. The experiments show that our representative set attains expected characteristics and captures information more efficiently.