We define a (non-decreasing) sequence {dTC(m)(X)}(m >= 2) of sequential versions of distributional topological complexity (dTC) of a space X introduced by Dranishnikov and Jauhari [5]. This sequence generalizes dTC...
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We define a (non-decreasing) sequence {dTC(m)(X)}(m >= 2) of sequential versions of distributional topological complexity (dTC) of a space X introduced by Dranishnikov and Jauhari [5]. This sequence generalizes dTC(X) in the sense that dTC(2)(X)=dTC(X), and is a direct analog to the well-known sequence {TCm(X)}(m >= 2). We show that like TCm and dTC, the sequential versions dTC(m) are also homotopy invariants. Furthermore, dTCm(X) relates with the distributional LS-category (dcat) of products of X in the same way as TCm(X) relates with the classical LS-category (cat) of products of X. On one hand, we show that in general, dTC(m) is a different concept than TCm for each m >= 2. On the other hand, by finding sharp cohomological lower bounds to dTC(m)(X), we provide various examples of closed manifolds X for which the sequences {TCm(X)}(m >= 2) and {dTC(m)(X)}(m >= 2) coincide. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
In this paper, we propose a novel distributed navigation algorithm for people to escape from critical event region in wireless sensor networks (WSNs). Unlike existing works, the scenario discussed in the paper has no ...
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ISBN:
(纸本)9781424492688
In this paper, we propose a novel distributed navigation algorithm for people to escape from critical event region in wireless sensor networks (WSNs). Unlike existing works, the scenario discussed in the paper has no goal or exit as guidance, leading to a big challenge for the navigation problem. To solve it, our proposed navigationalgorithm computes the convex hull of the event region just by some topological methods. With the reference of the convex hull, people can be easily navigated out of the event region. Both the computation complexity and communication overhead of the proposed algorithm are very low, as it only needs to flood two shortest path trees in a limited area around the event region with a distance [L/2 pi] + 1 to the event boundary, where L is the length of the boundary. Conducted simulations have verified the effectiveness and scalability of the proposed algorithm.
In an emergency, wireless network sensors combined with a navigationalgorithm could help safely guide people to a building exit while helping them avoid hazardous areas.
In an emergency, wireless network sensors combined with a navigationalgorithm could help safely guide people to a building exit while helping them avoid hazardous areas.
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