K-coverage in regular deterministic sensor deployments

An area is k-covered if every point of the area is covered by at least k sensors. K-coverage is necessary for many applications, such as intrusion detection, data gathering, and object tracking. It is also desirable in situations where a stronger environmental monitoring capability is desired, such as military applications. In this paper, we study the problem of k-coverage in deterministic homogeneous deployments of sensors. We examine the three regular sensor deployments - triangular, square and hexagonal deployments - for k-coverage of the deployment area, for k ≥ 1. We compare the three regular deployments in terms of sensor density. For each deployment, we compute an upper bound and a lower bound on the optimal distance of sensors from each other that ensure k-coverage of the area. We present the results for each k from 1 to 20 and show that the required number of sensors to k-cover the area using uniform random deployment is approximately 3-10 times higher than regular deployments

Efficient Matching of Substrings in Uncertain Sequences

Substring matching is fundamental to data mining methods for se-quential data. It involves checking the existence of a short subse-quence within a longer sequence, ensuring no gaps within a match. Whilst a large amount of existing work has focused on substring matching and mining techniques for certain sequences, there are on-ly a few results for uncertain sequences. Uncertain sequences pro-vide powerful representations for modelling sequence behavioural characteristics in emerging domains, such as bioinformatics, sen-sor streams and trajectory analysis. In this paper, we focus on the core problem of computing substring matching probability in un-certain sequences and propose an efficient dynamic programming algorithm for this task. We demonstrate our approach is both com-petitive theoretically, as well as effective and scalable experimental-ly. Our results contribute towards a foundation for adapting classic sequence mining methods to deal with uncertain data.

Efficient Cost Modeling of Space-filling Curves

A space-filling curve (SFC) maps points in a multi-dimensional spaceto one-dimensional points by discretizing the multi-dimensionalspace into cells and imposing a linear order on the cells. This way,an SFC enables the indexing of multi-dimensional data using a onedimensional index such as a B+-tree. Choosing an appropriate SFCis crucial, as different SFCs have different effects on query performance. Currently, there are two primary strategies: 1) deterministicschemes, which are computationally efficient but often yield suboptimal query performance, and 2) dynamic schemes, which considera broad range of candidate SFCs based on cost functions but incursignificant computational overhead. Despite these strategies, existing methods cannot efficiently measure the effectiveness of SFCsunder heavy query workloads and numerous SFC options.To address this problem, we propose means of constant-time costestimations that can enhance existing SFC selection algorithms, enabling them to learn more effective SFCs. Additionally, we proposean SFC learning method that leverages reinforcement learning andour cost estimation to choose an SFC pattern efficiently. Experimental studies offer evidence of the effectiveness and efficiency ofthe proposed means of cost estimation and SFC learning.A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables the indexing of multi-dimensional data using a one-dimensional index such as a B+-tree. Choosing an appropriate SFC is crucial, as different SFCs have different effects on query performance. Currently, there are two primary strategies: 1) deterministic schemes, which are computationally efficient but often yield suboptimal query performance, and 2) dynamic schemes, which consider a broad range of candidate SFCs based on cost functions but incur significant computational overhead. Despite these strategies, existing methods cannot efficiently measure the effectiveness of SFCs under heavy query workloads and numerous SFC options. To address this problem, we propose means of constant-time cost estimations that can enhance existing SFC selection algorithms, enabling them to learn more effective SFCs. Additionally, we propose an SFC learning method that leverages reinforcement learning and our cost estimation to choose an SFC pattern efficiently. Experimental studies offer evidence of the effectiveness and efficiency of the proposed means of cost estimation and SFC learning