In this paper, we give a simple method for determining the medians of a discrete set according to the Manhattan metric on ℤ2. We show how the medians can be determined by means of the discrete set's projections along the horizontal and vertical directions. Moreover, we prove that if the discrete set satisfies some connection and convexity constraints along the previous directions, the medians belong to the discrete set.
The medians of discrete sets / A. DEL LUNGO; M. NIVAT; R. PINZANI; L. SORRI;. - In: INFORMATION PROCESSING LETTERS. - ISSN 0020-0190. - STAMPA. - 65:(1998), pp. 293-299. [10.1016/s0020-0190(98)00020-9]
The medians of discrete sets
PINZANI, RENZO;
1998
Abstract
In this paper, we give a simple method for determining the medians of a discrete set according to the Manhattan metric on ℤ2. We show how the medians can be determined by means of the discrete set's projections along the horizontal and vertical directions. Moreover, we prove that if the discrete set satisfies some connection and convexity constraints along the previous directions, the medians belong to the discrete set.
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