Abstract
We show that seven discrete optimization problems from different fields of discrete mathematics (such as linear algebra, combinatorics, ] geometry, and functional analysis) that at first sight seem to be quite different prove to be in fact rather close to each other. This closeness enables us, given an algorithm for one problem, to construct an optimization or approximation algorithm for solving the other problems in the list. For each problem, an extremum function is defined which characterizes the performance of the optimal solution of the problem in the worst case. Relations between these extremum functions are derived.
Supported by the Russian Foundation for Fundamental Research (Grant 96-01-01591).
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Sevastianov, S. (1997). Seven problems: So different yet close. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_34
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DOI: https://doi.org/10.1007/3-540-63397-9_34
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