When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2017.74
URN: urn:nbn:de:0030-drops-80706
URL: http://drops.dagstuhl.de/opus/volltexte/2017/8070/
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### Computing the Maximum using (min, +) Formulas

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### Abstract

We study computation by formulas over (min,+). We consider the computation of max{x_1,...,x_n} over N as a difference of (min,+) formulas, and show that size n + n \log n is sufficient and necessary. Our proof also shows that any (min,+) formula computing the minimum of all sums of n-1 out of n variables must have n \log n leaves; this too is tight. Our proofs use a complexity measure for (min,+) functions based on minterm-like behaviour and on the entropy of an associated graph.

### BibTeX - Entry

```@InProceedings{mahajan_et_al:LIPIcs:2017:8070,
author =	{Meena Mahajan and Prajakta Nimbhorkar and Anuj Tawari},
title =	{{Computing the Maximum using (min, +) Formulas}},
booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
pages =	{74:1--74:11},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-046-0},
ISSN =	{1868-8969},
year =	{2017},
volume =	{83},
editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},