Lukas Kroc

Parametric probabilistic sensor network routing

Motivated by realistic sensor network scenarios that have misinformed nodes and variable network topologies, we propose a fundamentally different approach to routing that combines the best features of limited-flooding and information-sensitive path-finding protocols into a reliable, low-power method that can make delivery guarantees independent of parameter values or information noise levels. We introduce Parametric Probabilistic Sensor Network Routing Protocols, a family of light-weight and robust multi-path routing protocols for sensor networks in which an intermediate sensor decides to forward a message with a probability that depends on various parameters, such as the distance of the sensor to the destination, the distance of the source sensor to the destination, or the number of hops a packet has already traveled. We propose two protocol variants of this family and compare the new methods to other probabilistic and deterministic protocols, namely constant-probability gossiping, uncontrolled flooding, random wandering, shortest path routing (and a variation), and a load-spreading shortest-path protocol inspired by [Servetto, Barrenechea, 2002]. We consider sensor networks where a sensors knowledge of the local or global information is uncertain (parametrically noised) due to sensor mobility, and investigate the trade-off between robustness of the protocol as measured by quality of service (in particular, successful delivery rate and delivery lag) and use of resources (total network load). Our results show that the multi-path protocols are less sensitive to misinformation, and suggest that in the presence of noisy data, a limited flooding strategy will actually perform better and use fewer resources than an attempted single-path routing strategy, with the Parametric Probabilistic Sensor Network Routing Protocols outperforming other protocols. Our results also suggest that protocols using network information perform better than protocols that do not, even in the presence of strong noise.

Parametric probabilistic routing in sensor networks

Motivated by realistic sensor network scenarios that have mis-in-formed nodes and variable network topologies, we propose an approach to routing that combines the best features of limited-flooding and information-sensitive path-finding protocols into a reliable, low-power method that can make delivery guarantees independent of parameter values or information noise levels. We introduce Parametric Probabilistic Sensor Network Routing Protocols, a family of light-weight and robust multi-path routing protocols for sensor networks in which an intermediate sensor decides to forward a message with a probability that depends on various parameters, such as the distance of the sensor to the destination, the distance of the source sensor to the destination, or the number of hops a packet has already traveled. We propose two protocol variants of this family and compare the new methods to other probabilistic and deterministic protocols, namely constant-probability gossiping, uncontrolled flooding, random wandering, shortest path routing (and a variation), and a load-spreading shortest-path protocol inspired by (Servetto and Barrenechea, 2002). We consider sensor networks where a sensor’s knowledge of the local or global information is uncertain (parametrically noised) due to sensor mobility, and investigate the trade-off between robustness of the protocol as measured by quality of service (in particular, successful delivery rate and delivery lag) and use of resources (total network load). Our results for networks with randomly placed nodes and realistic urban networks with varying density show that the multi-path protocols are less sensitive to misinformation, and suggest that in the presence of noisy data, a limited flooding strategy will actually perform better and use fewer resources than an attempted single-path routing strategy, with the Parametric Probabilistic Sensor Network Routing Protocols outperforming other protocols. Our results also suggest that protocols using network information perform better than protocols that do not, even in the presence of strong noise.

Inference in particle tracking experiments by passing messages between images

Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and/or the density of the particles increases due to uncertainties on the trajectories that particles followed during the images’ acquisition time. Here, we report an efficient method for learning parameters of the dynamics of the particles from their positions in time-consecutive images. Our algorithm belongs to the class of message-passing algorithms, known in computer science, information theory, and statistical physics as belief propagation (BP). The algorithm is distributed, thus allowing parallel implementation suitable for computations on multiple machines without significant intermachine overhead. We test our method on the model example of particle tracking in turbulent flows, which is particularly challenging due to the strong transport that those flows produce. Our numerical experiments show that the BP algorithm compares in quality with exact Markov Chain Monte Carlo algorithms, yet BP is far superior in speed. We also suggest and analyze a random distance model that provides theoretical justification for BP accuracy. Methods developed here systematically formulate the problem of particle tracking and provide fast and reliable tools for the model’s extensive range of applications.

Message-passing and local heuristics as decimation strategies for satisfiability

Decimation is a simple process for solving constraint satisfaction problems, by repeatedly fixing variable values and simplifying without reconsidering earlier decisions. We investigate different decimation strategies, contrasting those based on local, syntactic information from those based on message passing, such as statistical physics based Survey Propagation (SP) and the related and more well-known Belief Propagation (BP). Our results reveal that once we resolve convergence issues, BP itself can solve fairly hard random k-SAT formulas through decimation; the gap between BP and SP narrows down quickly as k increases. We also investigate observable differences between BP/SP and other common CSP heuristics as decimation proceeds, exploring the hardness of the decimated formulas and identifying a somewhat unexpected feature of message passing heuristics, namely, unlike other heuristics for satisfiability, they avoid unit propagation as variables are fixed.

Leveraging belief propagation, backtrack search, and statistics for model counting

We consider the problem of estimating the model count (number of solutions) of Boolean formulas, and present two techniques that compute estimates of these counts, as well as either lower or upper bounds with different trade-offs between efficiency, bound quality, and correctness guarantee. For lower bounds, we use a recent framework for probabilistic correctness guarantees, and exploit message passing techniques for marginal probability estimation, namely, variations of Belief Propagation (BP). Our results suggest that BP provides useful information even on structured loopy formulas. For upper bounds, we perform multiple runs of the MiniSat SAT solver with a minor modification, and obtain statistical bounds on the model count based on the observation that the distribution of a certain quantity of interest is often very close to the normal distribution. Our experiments demonstrate that our model counters based on these two ideas, BPCount and MiniCount, can provide very good bounds in time significantly less than alternative approaches.

An empirical study of optimal noise and runtime distributions in local search

This paper presents a detailed empirical study of local search for Boolean satisfiability (SAT), highlighting several interesting properties, some of which were previously unknown or had only anecdotal evidence. Specifically, we study hard random 3-CNF formulas and provide surprisingly simple analytical fits for the optimal (static) noise level and the runtime at optimal noise, as a function of the clause-to-variable ratio. We also demonstrate, for the first time for local search, a power-law decay in the tail of the runtime distribution in the low noise regime. Finally, we discuss a Markov Chain model capturing this intriguing feature.

Probabilistic multi-path vs. deterministic single-path protocols for dynamic ad-hoc network scenarios

We investigate the performance of different protocol stacks under various application scenarios. Our method of choice is a full-fledged simulation in QualNet, testing the complete protocol stack over fairly large-scale networks. We find that the relative ranking of protocols strongly depends on the network scenario, the session load, the mobility level, and the choice of protocol parameters. We show that the Parametric Probabilistic Protocols, which we generalize from their original definition, can outperform standard routing protocols, such as AODV or Gossiping or Shortest-Path, in a variety of realistic scenarios.

SessionSim: activity-based session generation for network simulation

We present SessionSim, a tool for generating realistic communication sessions such as phone calls, http and email data traffic. Realistic data traffic is a crucial requirement to gauge the realism of any larger communication network simulation study. SessionSim is part of a large-scale communication network simulation environment (MIITS: Multi-scale Integrated Information and Telecommunications System), where detailed information about the individuals in a synthetic population is available, including activities (e.g., sleep, work, lunch) and locations. The key aspect of the SessionSim modeling philosophy is the insight that communication behavior heavily depends on the type of activity people are engaged in; key model parameters in addition to the nature of this dependence are inter-session times, source-destination pairs, and the actual data content that determines session size or duration. We present a mix of empirical data, earlier models and intuition for determining session parameters for phone calls, http and email and briefly discuss validation studies showing that our generated communication sessions adequately mimic real-world data. We also discuss our implementation of SessionSim in the scalable OO-simulation framework called SimCore.

Maneuverable relays to improve energy efficiency in sensor networks

We propose a hybrid model to alleviate the notorious problem of premature battery depletion in sensor networks: in a first stage, simple sensors are deployed over an area of interest using any traditional method, in a second phase, more powerful relays are put in positions that allow them to off-load as much of the forwarding burden imposed on the simple sensors as possible. We introduce this model in detail, give a few theoretical results with respect to the optimal placement of the powerful sensors, propose various heuristic approaches for their placement, and present comparative simulation results for these heuristics.