We consider the problem of deploying sensors in a large water distribution network, in order to detect the malicious introduction of contaminants. We show that a large class of realistic objective functions – such as reduction of detection time and the population protected from consuming contaminated water – exhibit an important diminishing returns effect called submodularity. We exploit the submodularity of these objectives in order to design efficient placement algorithms with provable performance guarantees. Our algorithms do not rely on mixed integer programming, and scale well to networks of arbitrary size. The problem instances considered in our approach are orders of magnitude (a factor of 72) larger than the largest problems solved in the literature. We show how our method can be extended to multicriteria optimization,

In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective functions. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NP-complete problems admit efficient algorithms. We show how our algorithm can be extended to handle complex cost functions (incorporating non-unit observation cost or communication and path costs). We also show how the algorithm can be used to near-optimally trade off expected-case (e.g., the Mean Square Prediction Error in Gaussian Process regression) and worst-case (e.g., maximum predictive variance) performance. We show that many important machine learning problems fit our robust submodular observation selection formalism, and provide extensive empirical evaluation on several real-world problems. For Gaussian Process regression, our algorithm compares favorably with state-of-the-art heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDP-based algorithms.

This paper examines the problem of locating a mobile, non-adversarial target in an indoor environment using multiple robotic searchers. One way to formulate this problem is to assume a known environment and choose searcher paths most likely to intersect with the path taken by the target. We refer to this as the Multi-robot Efficient Search Path Planning (MESPP) problem. Such path planning problems are NP-hard, and optimal solutions typically scale exponentially in the number of searchers. We present an approximation algorithm that utilizes finite-horizon planning and implicit coordination to achieve linear scalability in the number of searchers. We prove that solving the MESPP problem requires maximizing a nondecreasing, submodular objective function, which leads to theoretical bounds on the performance of our approximation algorithm. We extend our analysis by considering the scenario where searchers are given noisy non-line-of-sight ranging measurements to the target. For this scenario, we derive and integrate online Bayesian measurement updating into our framework. We demonstrate the performance of our framework in two large-scale simulated environments, and we further validate our results using data from a novel ultra-wideband ranging sensor. Finally, we provide an analysis that demonstrates the relationship between MESPP and the intuitive average capture time metric. Results show that our proposed linearly scalable approximation algorithm generates searcher paths competitive with those generated by exponential algorithms. 1

Abstract — In this paper, we examine the problem of locating a non-adversarial target using multiple robotic searchers. This problem is relevant to many applications in robotics including emergency response and aerial surveillance. Assuming a known environment, this problem becomes one of choosing searcher paths that are most likely to intersect with the path taken by the target. We refer to this as the Multi-robot Efficient Search Path Planning (MESPP) problem. Such path planning problems are NP-hard, and optimal solutions typically scale exponentially in the number of searchers. We present a finitehorizon path enumeration algorithm for solving the MESPP problem that utilizes sequential allocation to achieve linear scalability in the number of searchers. We show that solving the MESPP problem requires the maximization of a nondecreasing, submodular objective function, which directly leads to theoretical guarantees on paths generated by sequential allocation. We also demonstrate how our algorithm can run online to incorporate noisy measurements of the target’s position during search. We verify the performance of our algorithm both in simulation and in experiments with a novel radio sensor capable of providing range through walls. Our results show that our linearly scalable MESPP algorithm generates searcher paths competitive with those generated by exponential algorithms. I.

Abstract — Here we present an anytime algorithm for clearing an environment using multiple searchers. Prior methods in the literature treat multi-agent search as either a worst-case problem (i.e., clear an environment of an adversarial evader with potentially infinite speed), or an average-case problem (i.e., minimize average capture time given a model of the target’s motion). We introduce an algorithm that combines finite-horizon planning with spanning tree traversal methods to generate plans that clear the environment of a worst-case adversarial target and have good average-case performance considering a target motion model. Our algorithm is scalable to large teams of searchers and yields theoretically bounded average-case performance. We have tested our proposed algorithm through a large number of experiments in simulation and with a team of robot and human searchers in an office building. Our combined search algorithm both clears the environment and reduces average capture times by up to 75 % when compared to a purely worst-case approach. I.

We consider the problem of monitoring spatial phenomena, such as road speeds on a highway, using wireless sensors with limited battery life. A central question is to decide where to locate these sensors to best predict the phenomenon at the unsensed locations. However, given the power constraints, we also need to determine when to selectively activate these sensors in order to maximize the performance while satisfying lifetime requirements. Traditionally, these two problems of sensor placement and scheduling have been considered separately from each other; one first decides where to place the sensors, and then when to activate them. In this paper, we present an efficient algorithm, eSPASS, that simultaneously optimizes the placement and the schedule. We prove that eSPASS provides a constant-factor approximation to the optimal solution of this NP-hard optimization problem. A salient feature of our approach is that it obtains “balanced ” schedules that perform uniformly well over time, rather than only on average. We then extend the algorithm to allow for a smooth power-accuracy tradeoff. Our algorithm applies to complex settings where the sensing quality of a set of sensors is measured, e.g., in the improvement of prediction accuracy (more formally, to situations where the sensing quality function is submodular). We present extensive empirical studies on several sensing tasks, and our results show that simultaneously placing and scheduling gives drastically improved performance compared to separate placement and scheduling (e.g., a 33 % improvement in network lifetime on the traffic prediction task).

Abstract—Flow monitoring is used for a wide range of network management applications. Many such applications require that the monitoring infrastructure provide high flow coverage and support fine-grained network-wide objectives. Coordinated Sampling (cSamp) is a recent proposal that improves the monitoring capabilities of ISPs to address these demands. In this paper, we address a key deployment impediment for cSamp-like solutions–the need for routers to determine the Origin-Destination (OD) pair of each packet. In practice, however, this information is not available without expensive changes. We present a new framework called cSamp-T, in which each router uses only local information, instead of the OD-pair identifiers. Leveraging results from the theory of maximizing submodular set functions, cSamp-T provides near-ideal performance in maximizing the total flow coverage in the network. Further, with a small amount of targeted upgrades to a few routers, cSamp-T nearly optimally maximizes the minimum fractional coverage across all OD-pairs. We demonstrate these results on a range of real topologies. I.

Abstract: The problem of deploying sensors in a large water distribution network is considered, in order to detect the malicious introduction of contaminants. It is shown that a large class of realistic objective functions—such as reduction of detection time and the population protected from consuming contaminated water—exhibits an important diminishing returns effect called submodularity. The submodularity of these objectives is exploited in order to design efficient placement algorithms with provable performance guarantees. The algorithms presented in this paper do not rely on mixed integer programming, and scale well to networks of arbitrary size. The problem instances considered in the approach presented in this paper are orders of magnitude �a factor of 72 � larger than the largest problems solved in the literature. It is shown how the method presented here can be extended to multicriteria optimization, selecting placements robust to sensor failures and optimizing minimax criteria. Extensive empirical evidence on the effectiveness of the method presented in this paper on two benchmark distribution networks, and an actual drinking water distribution system of greater than 21,000 nodes, is presented.

Flow monitoring is increasingly used for a wide range of network security and anomaly detection applications. These applications require that flow monitoring infrastructures provide high flow coverage and be able to support fine-grained network-wide objectives. Coordinated Sampling (cSamp) is a recent proposal for improving the flow monitoring capabilities of ISPs to address these demands. In this paper, we address a key deployment impediment for cSamp-like solutions – the requirement that each router must determine the Origin-Destination (OD) pair of each packet it observes. We cast cSamp in a new framework called cSamp-T that enables us to apply powerful results from the theory of maximizing submodular set functions to build effective flow monitoring solutions in which each router works with only local information. We show that cSamp-T provides near-ideal performance in maximizing the total flow coverage in the network. Further, with a small amount of additional targeted provisioning or upgrading a small number of ingress routers to add OD-pair identifiers, cSamp-T obtains near-optimal maximization of the minimum fractional coverage across all OD-pairs. We demonstrate these results on a range of real topologies. From a practical perspective, these results are promising since they expand the applicability of cSamp-like solutions to ISPs where OD-pair identification is challenging and also provides an incremental deployment path for ISPs. Additionally, we believe that many of the techniques we develop here are more broadly applicable to other aspects of network management and measurement.

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