Greedy algorithm

About: Greedy algorithm is a research topic. Over the lifetime, 15347 publications have been published within this topic receiving 393945 citations.

An Information-Theoretic Approach to PMU Placement in Electric Power Systems

Abstract: This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional 'topological observability' based approaches, this paper advocates a much more refined, information-theoretic criterion, namely the mutual information (MI) between the PMU measurements and the power system states. The proposed MI criterion can not only include the full system observability as a special case, but also can rigorously model the remaining uncertainties in the power system states with PMU measurements, so as to generate highly informative PMU configurations. Further, the MI criterion can facilitate robust PMU placement by explicitly modeling probabilistic PMU outages. We propose a greedy PMU placement algorithm, and show that it achieves an approximation ratio of (1-1/e) for any PMU placement budget. We further show that the performance is the best that one can achieve in practice, in the sense that it is NP-hard to achieve any approximation ratio beyond (1-1/e). Such performance guarantee makes the greedy algorithm very attractive in the practical scenario of multi-stage installations for utilities with limited budgets. Finally, simulation results demonstrate near-optimal performance of the proposed PMU placement algorithm.

A greedy algorithm for bulk loading R-trees

Abstract: CM-line loading of R-trees is useful to improve node utilization and query performance. WTepresent an algorithm for bulk loading R-trees -r&id diifers horn previous ones in two aspects (a) it partitions input data into subtrees in a top-down fashion (based on the fact that splits close to the root are likely to have a greater impact on performance), (b) at each tree level, it considers all cuts orthogonal to the coordinate axes that result in packed trees and greedily picks those optimizing an arbitrary cost function. EMm.sive esperirnentation with both real and synthetic data indicate that for region data our algorithm requires up to three times fewer disk accesses than other algorithms. It is the method of choice for data with skew in locations, areas, or aspect ratios. Such data is common in practice. Let n = number of input rectangles Let S = maximumnumber of rectangles per subtree Let M = maximumnumber of entries per node Let f (rl, r2) be the “user-supplied” cost function If n < S return {stop condition} For each dimension d For each ordering considered in this dimension d For i from 1 to [n/iVfl – 1 Let B. = MSR of first i S rectangles Let B1 = MSR of the other rectangles Remember i if f(Bo, BI) is better valued Split input set and orderings at best position.

Scheduling freight trains traveling on complex networks

Abstract: In the US, freight railways are one of the major means to transport goods from ports to inland destinations. According to the Association of American Railroad’s study, rail companies move more than 40% of the nation’s total freight. Given the fact that the freight railway industry is already running without much excess capacity, better planning and scheduling tools are needed to effectively manage the scarce resources, in order to cope with the rapidly increasing demand for railway transportation. This research develops optimization-based approaches for scheduling of freight trains. Two mathematical formulations of the scheduling problem are first introduced. One assumes the path of each train, which is the track segments each train uses, is given and the other one relaxes this assumption. Several heuristics based on mixtures of the two formulations are proposed. The proposed algorithms are able to outperform two existing heuristics, namely a simple look-ahead greedy heuristic and a global neighborhood search algorithm, in terms of railway total train delay. For large networks, two algorithms based on the idea of decomposition are developed and are shown to significantly outperform two existing algorithms.

Optimal IDS Sensor Placement and Alert Prioritization Using Attack Graphs

Abstract: We optimally place intrusion detection system (IDS) sensors and prioritize IDS alerts using attack graph analysis. We begin by predicting all possible ways of penetrating a network to reach critical assets. The set of all such paths through the network constitutes an attack graph, which we aggregate according to underlying network regularities, reducing the complexity of analysis. We then place IDS sensors to cover the attack graph, using the fewest number of sensors. This minimizes the cost of sensors, including effort of deploying, configuring, and maintaining them, while maintaining complete coverage of potential attack paths. The sensor-placement problem we pose is an instance of the NP-hard minimum set cover problem. We solve this problem through an efficient greedy algorithm, which works well in practice. Once sensors are deployed and alerts are raised, our predictive attack graph allows us to prioritize alerts based on attack graph distance to critical assets.

Clustering to minimize the sum of cluster diameters

Abstract: We study the problem of clustering points in a metric space so as to minimize the sum of cluster diameters. Significantly improving on previous results, we present a primal-dual based constant factor approximation algorithm for this problem. We present a simple greedy algorithm that achieves a logarithmic approximation which also applies when the distance function is asymmetric. The previous best known result obtained a logarithmic approximation with a constant factor blowup in the number of clusters. We also obtain an incremental clustering algorithm that maintains a solution whose cost is at most a constant factor times that of optimal with a constant factor blowup in the number of clusters.