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.
Network packet classification is a key functionality provided by modern routers enabling many new network applications such as quality of service, access control and differentiated services. Using ternary content addressable memories (TCAMs) to perform high-speed packet classification has become the de facto standard in industry. However, despite their high speed, one major drawback of TCAMs is their high power consumption. Although SmartPC, the state-of-the-art technique, was proposed to reduce power consumption by constructing a pre-classifier to activate TCAM blocks selectively, its bottom-up approach restricts its ability of grouping rules into disjoint TCAM blocks. In this paper, we propose a top-down approach for two-stage TCAM-based packet classification. The novelty of our work is the intelligent combination of softwarebased packet classification with TCAM-based techniques. We start by constructing a set of decision-trees for the packet classification rules, which enable the subsequent steps an excellent global view on the relationships among rules. The decision-trees are then mapped to TCAM blocks with flexible heuristics. Our top-down framework addresses the bottlenecks (the number of general rules, which have to be activated unconditionally every time) of SmartPC very effectively. Using ClassBench in our experimentations, we show that our technique is able to restrict the number of general rules to just 1% of the overall rule set. This leads to a dramatic power reduction of up to 98%, and 96% on average, which significantly outperforms SmartPC.
We study the Maximum Satisfiability problem (MaxSAT). Particularly, we derive a branching algorithm of running time O*(1.2989^m) for the MaxSAT problem, where m denotes the number of clauses in the given CNF formula. Our algorithm considerably improves the previous best result O*(1.3248^m) by Chen and Kanj [2004] published 15 years ago. For our purpose, we derive improved branching strategies for variables of degrees 3, 4, and 5. The worst case of our branching algorithm is at variables of degree 4 which occur twice both positively and negatively in the given CNF formula. To serve the branching rules and shrink the size of the CNF formula, we also propose a variety of reduction rules which can be exhaustively applied in polynomial time and, moreover, some of them solve a bottleneck of the previous best algorithm.
The integrated satellite-terrestrial network has the characteristics of large scale, complex, high dynamic and heterogeneousness. Adopting traditional routing methods in the integrated satellite-terrestrial network will cause problems of poor scalability and large routing overhead. Greedy forwarding strategy based on network mapping with hyperbolic geometry works well in large scale network. However, there is no study on applying the network mapping with hyperbolic geometry to complex networks beyond two dimensions, including the integrated satellite-terrestrial network. Based on the method of spherical polar projection, this paper proposes a hyperbolic coordinates mapping algorithm in three-dimensional geographic space suitable for the integrated satellite-terrestrial network. This algorithm gives nodes of heterogeneous layers in the integrated satellite-terrestrial network a unified expression based on four-dimensional hyperbolic coordinates, which helps to quickly identify and locate nodes without global information distribution and scheduling when routing. The routing strategy using greedy forwarding strategy based on this algorithm only costs low storage overhead, as it does not need routing tables. Simulations demonstrate that the performance of the algorithm is hardly affected by the exponential expansion of the network size, which means the property of scalability is excellent. Also, it is stable under heterogeneous network structure, and maintains a stable routing success rate for optimal path selection around 93% with a time complexity of O(n).INDEX TERMS Integrated satellite-terrestrial network, hyperbolic geometry, network mapping, greedy forwarding.
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