Local algorithms for edge colorings in UDGs

AbstractIn this paper, we consider two problems: the edge coloring and the strong edge coloring problems on unit disk graphs (UDGs). Both problems have important applications in wireless sensor networks as they can be used to model link scheduling problems in such networks. It is well known that both problems are NP-complete, and approximation algorithms for them have been extensively studied under the centralized model of computation. Centralized algorithms, however, are not suitable for ad hoc wireless sensor networks whose devices typically have limited resources, and lack the centralized coordination.We develop local distributed approximation algorithms for the edge coloring and the strong edge coloring problems on unit disk graphs. For the edge coloring problem, our local distributed algorithm has approximation ratio 2 and locality 50. For the strong edge coloring problem on UDGs, we present two local distributed algorithms with different tradeoffs between their approximation ratio and locality. The first algorithm has ratio 128 and locality 22, whereas the second algorithm has ratio 10 and locality 180

Two Timescale Convergent Q-learning for Sleep--Scheduling in Wireless Sensor Networks

In this paper, we consider an intrusion detection application for Wireless Sensor Networks (WSNs). We study the problem of scheduling the sleep times of the individual sensors to maximize the network lifetime while keeping the tracking error to a minimum. We formulate this problem as a partially-observable Markov decision process (POMDP) with continuous state-action spaces, in a manner similar to (Fuemmeler and Veeravalli [2008]). However, unlike their formulation, we consider infinite horizon discounted and average cost objectives as performance criteria. For each criterion, we propose a convergent on-policy Q-learning algorithm that operates on two timescales, while employing function approximation to handle the curse of dimensionality associated with the underlying POMDP. Our proposed algorithm incorporates a policy gradient update using a one-simulation simultaneous perturbation stochastic approximation (SPSA) estimate on the faster timescale, while the Q-value parameter (arising from a linear function approximation for the Q-values) is updated in an on-policy temporal difference (TD) algorithm-like fashion on the slower timescale. The feature selection scheme employed in each of our algorithms manages the energy and tracking components in a manner that assists the search for the optimal sleep-scheduling policy. For the sake of comparison, in both discounted and average settings, we also develop a function approximation analogue of the Q-learning algorithm. This algorithm, unlike the two-timescale variant, does not possess theoretical convergence guarantees. Finally, we also adapt our algorithms to include a stochastic iterative estimation scheme for the intruder's mobility model. Our simulation results on a 2-dimensional network setting suggest that our algorithms result in better tracking accuracy at the cost of only a few additional sensors, in comparison to a recent prior work

Deep Reinforcement Learning for Wireless Sensor Scheduling in Cyber-Physical Systems

In many Cyber-Physical Systems, we encounter the problem of remote state estimation of geographically distributed and remote physical processes. This paper studies the scheduling of sensor transmissions to estimate the states of multiple remote, dynamic processes. Information from the different sensors have to be transmitted to a central gateway over a wireless network for monitoring purposes, where typically fewer wireless channels are available than there are processes to be monitored. For effective estimation at the gateway, the sensors need to be scheduled appropriately, i.e., at each time instant one needs to decide which sensors have network access and which ones do not. To address this scheduling problem, we formulate an associated Markov decision process (MDP). This MDP is then solved using a Deep Q-Network, a recent deep reinforcement learning algorithm that is at once scalable and model-free. We compare our scheduling algorithm to popular scheduling algorithms such as round-robin and reduced-waiting-time, among others. Our algorithm is shown to significantly outperform these algorithms for many example scenarios

Minimizing Flow Time in the Wireless Gathering Problem

We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than \Omega(m^{1/3) when $m$ packets have to be transmitted, unless $P = NP$. We then use resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to

Coordination of Mobile Mules via Facility Location Strategies

In this paper, we study the problem of wireless sensor network (WSN) maintenance using mobile entities called mules. The mules are deployed in the area of the WSN in such a way that would minimize the time it takes them to reach a failed sensor and fix it. The mules must constantly optimize their collective deployment to account for occupied mules. The objective is to define the optimal deployment and task allocation strategy for the mules, so that the sensors' downtime and the mules' traveling distance are minimized. Our solutions are inspired by research in the field of computational geometry and the design of our algorithms is based on state of the art approximation algorithms for the classical problem of facility location. Our empirical results demonstrate how cooperation enhances the team's performance, and indicate that a combination of k-Median based deployment with closest-available task allocation provides the best results in terms of minimizing the sensors' downtime but is inefficient in terms of the mules' travel distance. A k-Centroid based deployment produces good results in both criteria.Comment: 12 pages, 6 figures, conferenc