Parameterized Approaches for Large-Scale Optimization Problems

In this dissertation, we study challenging discrete optimization problems from the perspective of parameterized complexity. The usefulness of this type of analysis is twofold. First, it can lead to efficient algorithms for large-scale problem instances. Second, the analysis can provide a rigorous explanation for why challenging problems might appear relatively easy in practice. We illustrate the approach on several different problems, including: the maximum clique problem in sparse graphs; 0-1 programs with many conflicts; and the node-weighted Steiner tree problem with few terminal nodes. We also study polyhedral counterparts to fixed-parameter tractable algorithms. Specifically, we provide fixed-parameter tractable extended formulations for independent set in tree-like graphs and for cardinality-constrained vertex covers

Energy efficient clustering and secure data aggregation in wireless sensor networks

Communication consumes the majority of a wireless sensor network\u27s limited energy. There are several ways to reduce the communication cost. Two approaches used in this work are clustering and in-network aggregation. The choice of a cluster head within each cluster is important because cluster heads use additional energy for their responsibilities and that burden needs to be carefully distributed. We introduce the energy constrained minimum dominating set (ECDS) to model the problem of optimally choosing cluster heads in the presence of energy constraints. We show its applicability to sensor networks and give an approximation algorithm of O(log n) for solving the ECDS problem. We propose a distributed algorithm for the constrained dominating set which runs in O(log n log [triangle]) rounds with high probability. We show experimentally that the distributed algorithm performs well in terms of energy usage, node lifetime, and clustering time and thus is very suitable for wireless sensor networks. Using aggregation in wireless sensor networks is another way to reduce the overall communication cost. However, changes in security are necessary when in- network aggregation is applied. Traditional end-to-end security is not suitable for use with in-network aggregation. A corrupted sensor has access to the intermediate data and can falsify results. Additively homomorphic encryption allows for aggregation of encrypted values, with the result being the same as the result as if unencrypted data were aggregated. Using public key cryptography, digital signatures can be used to achieve integrity. We propose a new algorithm using homomorphic encryption and additive digital signatures to achieve confidentiality, integrity and availability for in- network aggregation in wireless sensor networks. We prove that our digital signature algorithm which is based on Elliptic Curve Digital Signature Algorithm (ECDSA) is at least as secure as ECDSA. Even without in-network aggregation, security is a challenge in wireless sensor networks. In wireless sensor networks, not all messages need to be secured with the same level of encryption. We propose a new algorithm which provides adequate levels of security while providing much higher availablility [sic] than other security protocols. Our approach uses similar amounts of energy as a network without security --Abstract, page iv

Self-stabilizing k-clustering in mobile ad hoc networks

In this thesis, two silent self-stabilizing asynchronous distributed algorithms are given for constructing a k-clustering of a connected network of processes. These are the first self-stabilizing solutions to this problem. One algorithm, FLOOD, takes O( k) time and uses O(k log n) space per process, while the second algorithm, BFS-MIS-CLSTR, takes O(n) time and uses O(log n) space; where n is the size of the network. Processes have unique IDs, and there is no designated leader. BFS-MIS-CLSTR solves three problems; it elects a leader and constructs a BFS tree for the network, constructs a minimal independent set, and finally a k-clustering. Finding a minimal k-clustering is known to be NP -hard. If the network is a unit disk graph in a plane, BFS-MIS-CLSTR is within a factor of O(7.2552k) of choosing the minimal number of clusters; A lower bound is given, showing that any comparison-based algorithm for the k-clustering problem that takes o( diam) rounds has very bad worst case performance; Keywords: BFS tree construction, K-clustering, leader election, MIS construction, self-stabilization, unit disk graph

The Complexity of Finding Effectors

The NP-hard EFFECTORS problem on directed graphs is motivated by applications in network mining, particularly concerning the analysis of probabilistic information-propagation processes in social networks. In the corresponding model the arcs carry probabilities and there is a probabilistic diffusion process activating nodes by neighboring activated nodes with probabilities as specified by the arcs. The point is to explain a given network activation state as well as possible by using a minimum number of "effector nodes"; these are selected before the activation process starts. We correct, complement, and extend previous work from the data mining community by a more thorough computational complexity analysis of EFFECTORS, identifying both tractable and intractable cases. To this end, we also exploit a parameterization measuring the "degree of randomness" (the number of "really" probabilistic arcs) which might prove useful for analyzing other probabilistic network diffusion problems as well.Comment: 28 page

Energy-efficient coverage with wireless sensors

Many sensor networks are deployed for the purpose of covering and monitoring a particular region, and detecting the object of interest in the region. In these applications, coverage is one of the centric problems in sensor networks. Such problem is centered around a basic question: ``How well can the sensors observe the physical world?\u27\u27 The concept of coverage can be interpreted as a measure of quality of service provided by the sensing function in various ways depending on sensor devices and applications. On the other hand, sensor nodes are usually battery-powered and subject to limitations based on the available battery energy. It is, therefore, critical to design, deploy and operate a wireless sensor network in an energy-efficient manner, while satisfying the coverage requirement. In order to prolong the lifetime of a sensor network, we explore the notion of connected-k-coverage in sensor networks. It requires the monitored region to be k-covered by a connected component of active sensors, which is less demanding than requiring k-coverage and connectivity among all active sensors simultaneously. We investigate the theoretical foundations about connected-k-coverage and, by using the percolation theorem, we derive the critical conditions for connected-k-coverage for various relations between sensors\u27 sensing radius and communication range. In addition, we derive an effective lower bound on the probability of connected-k-coverage, and propose a simple randomized scheduling algorithm and select proper operational parameters to prolong the lifetime of a large-scale sensor network. It has been shown that sensors\u27 collaboration (information fusion) can improve object detection performance and area coverage in sensor networks. The sensor coverage problem in this situation is regarded as information coverage. Based on a probabilistic sensing model, we study the object detection problem and develop a novel on-demand framework (decision fusion-based) for collaborative object detection in wireless sensor networks, where inactive sensors can be triggered by nearby active sensors to collaboratively sense and detect the object. By using this framework, we can significantly improve the coverage performance of the sensor networks, while the network power consumption can be reduced. Then, we proceed to study the barrier information coverage problem under the similar assumption that neighboring sensors may collaborate with each other to form a virtual sensor which makes the detection decision based on combined sensed readings. We propose both centralized and distributed schemes to operate a sensor network to information-cover a barrier efficiently. At last, we propose and study a multi-round sensor deployment strategy based on line-based sensor deployment model, which can use the fewest sensors to cover a barrier. We have an interesting discovery that the optimal two-round sensor deployment strategy yields the same barrier coverage performance as other optimal strategies with more than two rounds. This result is particularly encouraging as it implies that the best barrier coverage performance can be achieved with low extra deployment cost by deploying sensors in two rounds. In addition, two practical solutions are presented to deal with realistic situations when the distribution of a sensor\u27s residence point is not fully known

Parameterized algorithms of fundamental NP-hard problems: a survey

Parameterized computation theory has developed rapidly over the last two decades. In theoretical computer science, it has attracted considerable attention for its theoretical value and significant guidance in many practical applications. We give an overview on parameterized algorithms for some fundamental NP-hard problems, including MaxSAT, Maximum Internal Spanning Trees, Maximum Internal Out-Branching, Planar (Connected) Dominating Set, Feedback Vertex Set, Hyperplane Cover, Vertex Cover, Packing and Matching problems. All of these problems have been widely applied in various areas, such as Internet of Things, Wireless Sensor Networks, Artificial Intelligence, Bioinformatics, Big Data, and so on. In this paper, we are focused on the algorithms’ main idea and algorithmic techniques, and omit the details of them