Min Kyung An

On construction of quality fault-tolerant virtual backbone in wireless networks

In this paper, we study the problem of computing quality fault-tolerant virtual backbone in homogeneous wireless network, which is defined as the k-connected m-dominating set problem in a unit disk graph. This problem is NP-hard, and thus many efforts have been made to find a constant factor approximation algorithm for it, but never succeeded so far with arbitrary k ≥ 3 and m ≥ 1 pair. We propose a new strategy for computing a smaller-size 3-connected m-dominating set in a unit disk graph with any m ≥ 1. We show the approximation ratio of our algorithm is constant and its running time is polynomial. We also conduct a simulation to examine the average performance of our algorithm. Our result implies that while there exists a constant factor approximation algorithm for the k-connected m-dominating set problem with arbitrary k ≤ 3 and m ≥ 1 pair, the k-connected m-dominating set problem is still open with k > 3.

Minimum latency data aggregation in the physical interference model

Data aggregation has been the focus of many researchers as one of the most important applications in Wireless Sensor Networks. A main issue of data aggregation is how to construct efficient schedules by which data can be aggregated without any interference. The problem of constructing minimum latency data aggregation schedules (MLAS) has been extensively studied in the literature although most of existing works use the graph-based interference model. In this paper, we study the MLAS problem in the more realistic physical model known as signal-to-interference-noise-ratio (SINR). We first derive an @Wlogn approximation lower bound for the MLAS problem in the metric SINR model. We also prove the NP-hardness of the decision version of MLAS in the geometric SINR model. This is a significant contribution as these results have not been obtained before for the SINR model. In addition, we propose two constant factor approximation algorithms whose latency is bounded by O(@D+R) for the dual power model, where @D is the maximum node degree of a network and R is the network radius. Finally we study the performance of the algorithms through simulation.

Dual power assignment optimization for k-edge connectivity in WSNs

Power consumption is one of the crucial issues in Wireless Sensor Networks (WSNs). It therefore has been the focus of many researchers. An important problem concerning power consumption is how to minimize the number of maximum power nodes while maintaining a desired network topology. As fault tolerance is vitally important in practice, it is desirable that the constructed network topology is k-edge-connected (or k-connected). In this paper, we study the dual power assignment problem for k-edge connectivity (kEDP) in WSNs. While other studies consider only the special case k=2, our goal is to address the general problem. We prove the NP-completeness of kEDP problem in the geometric case and provide a 2-approximation algorithm using linear programming techniques. To our knowledge, this approximation ratio is currently the best one. We also introduce a heuristic whose performance is better compared with an approximation algorithm in [1].

Scheduling problems in interference-aware wireless sensor networks

In this paper, we study the Minimum Latency Aggregation Scheduling problem in two interference models, the collision-interference-free graph model and the physical interference model known as Signal-to-Interference-Noise-Ratio (SINR), with power control. The main issue is to compute schedules with the minimum number of timeslots such that data can be aggregated without any collision or interference. While existing works studied the problem under the uniform power model or the unlimited power model, we investigate the problem assuming a more realistic non-uniform power assignment where the maximum power level is bounded. We propose a constant factor approximation algorithm with O(R + X) timeslots, where R is the network radius and X is the link length diversity. Under a reasonable assumption about the link length diversity, the number of timeslots is bounded by O(R + log n) which gives a constant approximation ratio since the lower bound is max{ R, log n}, where n is the number of nodes. Along with the problem of constructing minimum latency data aggregation schedules, we also study two other related optimization problems, namely the Scheduling and Weighted One-Shot Scheduling problems with power control in the SINR model, and provide constant approximation algorithms.

Antenna orientation and range assignment in WSNs with directional antennas

Consider a set S of nodes in the plane such that the unit-disk graph G(S) spanning all nodes is connected. Each node in S is equipped with a directional antenna with beam-width θ = π/2. The objective of the Directional Antenna Orientation (AO) problem concerning symmetric connectivity is to determine an orientation of the antennas with a minimum transmission power range r = O(1) such that the induced symmetric communication graph is connected. Another related problem is the Antenna Orientation and Power Assignment (AOPA) problem whose objective is to assign each node u ϵ S an orientation of its antenna as well as a range r(u) such that the induced symmetric communication graph is connected and the total power assigned ΣuϵSr(u)β is minimized, where β ≥ 1 is the distance-power gradient (typically 2 ≤ β ≤ 5). In this paper, we study both problems by first proving that they are NP-hard. To the best of our knowledge, these NP-hardness results have not been obtained before in the literature. We then propose an algorithm for the AO problem that orients the antennas to yield a symmetric connected graph where the transmission power range is bounded by 9 which is currently the best result for this problem. (Previous bound for this problem is 14√2 by Aschner et al). We also propose a constant-approximation algorithm for the AOPA problem where our constant is smaller than the one in Aschner et als algorithm.

Symmetric connectivity in Wireless Sensor Networks with directional antennas

In this paper, we study the Antenna Orientation (AO) problem concerning symmetric connectivity in Directional Wireless Sensor Networks. We are given a set of nodes each of which is equipped with one directional antenna with beam-width θ = 2π/3 and is initially assigned a transmission range 1 that yields a connected unit disk graph spanning all nodes. The objective of the problem is to compute an orientation of the antennas and to find a minimum transmission power range r = O(1) such that the induced symmetric communication graph is connected. We propose an algorithm that orients the antennas to yield a symmetric connected graph where the transmission power range is bounded by 6 which is currently the best result for this problem. We also study the performance of our algorithm through simulation.

Dual power assignment optimization and fault tolerance in WSNs

Because of limited battery equipped on each sensor, power consumption is one of the crucial issues in wireless sensor networks (WSNs). It therefore has been the focus of many researchers. An important problem concerning power consumption is to minimize the number of maximum-power nodes while maintaining a desired network topology. As fault tolerance is vitally important in practice, it is desirable that the constructed network topology is

A note on the complexity of minimum latency data aggregation scheduling with uniform power in physical interference model

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