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We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Statistics for Spatial Data.

Social Network Analysis

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

A critical aspect of applications with wireless sensor networks is network lifetime. Power-constrained wireless sensor networks are usable as long as they can communicate sensed data to a processing node. Sensing and communications consume energy, therefore judicious power management and sensor scheduling can effectively extend network lifetime. To cover a set of targets with known locations when ground access in the remote area is prohibited, one solution is to deploy the sensors remotely, from an aircraft. The lack of precise sensor placement is compensated by a large sensor population deployed in the drop zone, that would improve the probability of target coverage. The data collected from the sensors is sent to a central node (e.g. cluster head) for processing. In this paper we propose un efficient method to extend the sensor network life time by organizing the sensors into a maximal number of set covers that are activated successively. Only the sensors from the current active set are responsible for monitoring all targets and for transmitting the collected data, while all other nodes are in a low-energy sleep mode. By allowing sensors to participate in multiple sets, our problem formulation increases the network lifetime compared with related work [M. Cardei et al], that has the additional requirements of sensor sets being disjoint and operating equal time intervals. In this paper we model the solution as the maximum set covers problem and design two heuristics that efficiently compute the sets, using linear programming and a greedy approach. Simulation results are presented to verify our approaches.

/pdf/energy-efficient-target-coverage-in-wireless-sensor-networks-2snkcx2hjq.pdf

Energy-efficient target coverage in wireless sensor networks

A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum-connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum-connected dominating set in unit-disk graphs. In this paper, we design a (1 + 1/s)-approximation for the minimum-connected dominating set in unit-disk graphs, running in time nO((s log s)2). © 2003 Wiley Periodicals, Inc.

/pdf/a-polynomial-time-approximation-scheme-for-the-minimum-3j8399mz19.pdf

A Polynomial-Time Approximation Scheme for the Minimum-Connected Dominating Set in Ad Hoc Wireless Networks

Minimum connected dominating sets and maximal independent sets in unit disk graphs

This paper targets the identification of outlying sensors (that is, outlying reading sensors) and the detection of the reach of events in sensor networks. Typical applications include the detection of the transportation front line of some vegetation or animalcule's growth over a certain geographical region. We propose and analyze two novel algorithms for outlying sensor identification and event boundary detection. These algorithms are purely localized and, thus, scale well to large sensor networks. Their computational overhead is low, since only simple numerical operations are involved. Simulation results indicate that these algorithms can clearly detect the event boundary and can identify outlying sensors with a high accuracy and a low false alarm rate when as many as 20 percent sensors report outlying readings. Our work is exploratory in that the proposed algorithms can accept any kind of scalar values as inputs?a dramatic improvement over existing work, which takes only 0/1 decision predicates. Therefore, our algorithms are generic. They can be applied as long as "events? can be modeled by numerical numbers. Though designed for sensor networks, our algorithms can be applied to the outlier detection and regional data analysis in spatial data mining.

/pdf/localized-outlying-and-boundary-data-detection-in-sensor-46x20cy01r.pdf

Localized Outlying and Boundary Data Detection in Sensor Networks

Contributing Authors Preface SECTION I. Network Design and Network Modelling Chapter 1. A Taxonomy-based Approach to Design Large-scale Sensor Networks (Aravind Iyer, Sunil S. Kulkarni, Vivek Mhatre and Catherine P. Rosenberg) Chapter 2. Algorithms for Robotic Deployment of WSN in Adaptive Sampling Applications (Dan O. Popa and Frank L. Lewis) Chapter 3. A Scalable Graph Model and Coordination Algorithms for Mobile Sensor Networks (Jindong Tan) SECTION II. Network Management Chapter 4. Medium Access Control Protocols for Wireless Sensor Networks (Ali Abu-el Humos, Mihaela Cardei, Bassem Alhalabi and Sam Hsu) Chapter 5. Topology Control for Wireless Sensor Networks (Yu Wang) Chapter 6. Boundary Detection for Sensor Networks (Ren-Shiou Liu, Lifeng Sang and Prasun Sinha) Chapter 7. TPSS: A Time-based Positioning Scheme for Sensor Networks with Short Range Beacons (Fang Liu, Xiuzhen Cheng, Dong Hua and Dechang Chen) Chapter 8. Wakeup Strategies in Wireless Sensor Networks (Curt Schurgers) Chapter 9. Time-Synchronization Challenges and Techniques (Weilian Su) Chapter 10. Location Service, Information Dissemination and Object Tracking in Wireless Sensor Networks by Using Quorum Methods (Dan-Dan Liu and Xiao-Hua Jia) Chapter 11. Maximizing the Lifetime of an Always-On Wireless Sensor Network Application: A Case Study (Santosh Kumar, Anish Arora and Ten H. Lai) SECTION III. Data Management Chapter 12. Data Management in Sensor Networks (Jinbao Li, Zhipeng Cai and Jianzhong Li) Chapter 13. Time-Synchronization Challenges and Techniques (Kai-Wei Fan, Sha Liu and Prasun Sinha) Chapter 14. Performance Comparison of Clustering Schemes in Sensor Networks (Yadi Ma and Maggie Cheng) Chapter 15. Reliable and Efficient Information Forwarding and Traffic Engineering in Wireless Sensor Networks (Fernand S. Cohen, Joshua Goldberg and Jaudelice C. de Oliveira) Chapter 16. Modeling Data Gathering in Wireless Sensor Networks (Bhaskar Krishnamachari) SECTION IV. Security Chapter 17. A Survey on Sensor Network Security (Xiaojiang Du and Yang Xiao) Chapter 18. A Passive Approach to Unauthorized Sensor Node Identication (Cherita Corbett, John Copeland and Raheem Beyah)

/pdf/wireless-sensor-networks-and-applications-3eyt0mhqmx.pdf

Weili Wu

Papers

Energy-efficient target coverage in wireless sensor networks

A Polynomial-Time Approximation Scheme for the Minimum-Connected Dominating Set in Ad Hoc Wireless Networks

Minimum connected dominating sets and maximal independent sets in unit disk graphs

Localized Outlying and Boundary Data Detection in Sensor Networks

Wireless Sensor Networks and Applications