![]() ![]() Suppose that we have constructed k ISTs rooted at a node r in a network. Particularly, the construction of independent spanning trees (ISTs), a kind of MSTs, is important because of the applications to fault-tolerant broadcasting and secure message distribution in reliable networks . However, MSTs are hard to configure in practice because optimizing MSTs with specific objectives in networks is a challenging combinatorial problem, e.g., see . Remarkably, the diameter of the constructed ISTs is about twice the diameter of Q n.Ĭonstructing multiple spanning trees (MSTs) in networks has recently been studied from a theoretical perspective and in real applications. Consequently, we can implement the algorithm for constructing n ISTs in O ( n N ) time, where N = n 2 n is the number of vertices of n-dimensional HSDC or parallelize the algorithm in O ( n ) time using N processors. Unlike most algorithms of recursively constructing tree structures, our algorithm can find every node’s parent in each spanning tree directly via an easy computation relied upon only the node address and tree index. Then, by the structure that n-dimensional HSDC is a compound graph of an n-dimensional hypercube Q n and n-clique K n, we amend the algorithm constructing ISTs for Q n to obtain the algorithm required by HSDC. We first establish the vertex-symmetry of HSDC. Regarding multiple spanning trees as routing protocol, ISTs have applications in data transmission, e.g., fault-tolerant broadcasting and secure message distribution. This paper investigates the construction of independent spanning trees (ISTs for short), a set of the rooted spanning trees associated with the disjoint-path property, in HSDC. For example, a server-centric DCN can initiate routing for data transmission. ![]() There is much to be gained by ensuring that law enforcement refrains from practicing parallel construction in the future.An emerging datacenter network (DCN) with high scalability called HSDC is a server-centric DCN that can help cloud computing in supporting many inherent cloud services. ![]() As this Article explains, using this process is a deliberate attempt to bypass constitutional guarantees in ways that will unduly prejudice criminal proceedings. Parallel construction enables law enforcement agencies to engage in questionable investigative practices, the concealment of which deprives criminal defendants of any challenges they might raise and prevents courts from reviewing the constitutionality of the practice in the first place.Īddressing parallel construction is a pressing issue, especially in light of the current events surrounding the 2013 global surveillance disclosures by Edward Snowden, the ongoing War on Drugs and War on Terror, and the efforts to reform the criminal justice system. It also undermines fundamental principles of due process. The result: parallel construction insulates surveillance techniques from judicial review, undermines checks and balances, and deprives individuals of the privacy benefits that court review would require. Parallel construction allows law enforcement agencies to capitalize on sensitive or secret national security techniques in the domestic criminal context, without any form of oversight or accountability. Clandestinely used for decades, this process raises serious constitutional questions. The process is undertaken to conceal the original source of evidence, which may have been obtained unlawfully. Parallel construction is the process of building a separate - and parallel - evidentiary basis for a criminal investigation. Federal law enforcement agencies are increasingly relying on "parallel construction" to pursue criminal cases against U.S. ![]()
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