Optimal Cuts and Bisections on the Real Line in Polynomial Time

Marek Karpinski; Andrzej Lingas; Dzmitry Sledneu

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arXiv · 1207.0933

Optimal Cuts and Bisections on the Real Line in Polynomial Time

Marek Karpinski·Andrzej Lingas·Dzmitry Sledneu

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Abstract

The exact complexity of geometric cuts and bisections is the longstanding open problem including even the dimension one. In this paper, we resolve this problem for dimension one (the real line) by designing an exact polynomial time algorithm. Our results depend on a new technique of dealing with metric equalities and their connection to dynamic programming. The method of our solution could be also of independent interest.

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BibTeX RIS

Marek Karpinski, Andrzej Lingas, Dzmitry Sledneu. 2012-07-04. Optimal Cuts and Bisections on the Real Line in Polynomial Time. https://arxiv.org/abs/1207.0933

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