An algorithm complexity is a very crucial issue in the algorithm design, especially if large data sets are to be processed. Data search is very often used in many algorithms and hash function use gives us a possibility to speed up the process significantly. Nevertheless, it is very difficult do design a good hash function especially for geometric applications. This paper describes a new hash function, its behaviour and use for non-trivial problems. Some problems can be solved effectively using

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... he principle of duality and the hash data structure. Also some problems that cannot be solved in Euclidean space can be solved if dual representation is used and some examples are presented, too.