The placement of text on a map to maximize map legibility, while avoiding graphic overplotting, is a problem in combinatorial optimization. This particular optimization problem can be formulated as a multiple choice integer programming problem, and the integer programming problem has a structure that can be exploited, using a Lagrangian heuristic, to obtain a cost effective solution, even when tens of thousands of variables and thousands of constraints are involved. This paper presents the mathematical formulation of the map label placement problem and describes a computer program implemented to solve it.
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Steven Zoraster (1990) studied this question.
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