Abstract
In our paper we discuss how elements of algebraic hyperstructure theory can be used in the context of underwater wireless sensor networks (UWSN). We present a mathematical model which makes use of the fact that when deploying nodes or operating the network we, from the mathematical point of view, regard an operation (or a hyperoperation) and a binary relation. In this part of the paper we relate our context to already existing topics of the algebraic hyperstructure theory such as quasi-order hypergroups, E L -hyperstructures, or ordered hyperstructures. Furthermore, we make use of the theory of quasi-automata (or rather, semiautomata) to relate the process of UWSN data aggregation to the existing algebraic theory of quasi-automata and their hyperstructure generalization. We show that the process of data aggregation can be seen as an automaton, or rather its hyperstructure generalization, with states representing stages of the data aggregation process of cluster protocols and describing available/used memory capacity of the network.
Highlights
Underwater wireless sensor networks (UWSN) are often used in environment monitoring where they review how human activities affect marine ecosystems, undersea explorations such as detecting oilfields, for disaster prevention, e.g., when monitoring ocean currents, in assisted navigation for the location of dangerous rocks in shallow waters, or for disturbed tactical surveillance for intrusion detection.The fact that such wireless sensor networks are deployed underwater results in profound differences from terrestrial wireless sensor networks
Further on we discuss three of these: EL–hyperstructures, quasi-order hypergroups, and ordered hyperstructures. Each of these concepts uses somewhat different background and assumptions: EL–hyperstructures are constructed from pre- and partially-ordered semigroups, i.e., the hyperoperation is defined using an operation and a relation compatible with it; Quasi-order hypergroups are constructed from pre-ordered sets, i.e., the hyperoperation is defined using a relation only; Ordered hyperstructures are algebraic hyperstructures on which a relation compatible with the hyperoperation is defined
If we look at the problem of data aggregation from the point of view of the automata theory, where every step is an application of the transition function with the initial state "data aggregation to begin" and the desirable state "data from all elements collected", we should be interested in constructing such automata or studying their properties
Summary
Underwater wireless sensor networks (UWSN) are often used in environment monitoring where they review how human activities affect marine ecosystems, undersea explorations such as detecting oilfields, for disaster prevention, e.g., when monitoring ocean currents, in assisted navigation for the location of dangerous rocks in shallow waters, or for disturbed tactical surveillance for intrusion detection. A common cluster based network consists of a centralized station deployed at the surface of the sea called a sink (or surface station) and sensor nodes deployed at various tiers inside the sea environment Each of these concepts uses somewhat different background and assumptions: EL–hyperstructures are constructed from pre- and partially-ordered semigroups, i.e., the hyperoperation is defined using an operation and a relation compatible with it; Quasi-order hypergroups are constructed from pre-ordered sets, i.e., the hyperoperation is defined using a relation only; Ordered hyperstructures are algebraic hyperstructures on which a relation compatible with the hyperoperation is defined All of these have been studied in depth and numerous results have been achieved in their respective theories. For this reason, closed intervals will not be denoted by [ a, b] but by h a; bi
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