Open AccessThe Geometric Traveling Salesman Problem in the Heisenberg Group
Author(s) -
Fausto Ferrari,
Bruno Franchi,
Hervé Pajot
Publication year - 2007
Publication title -
revista matemática iberoamericana
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.569
H-Index - 52
eISSN - 2235-0616
pISSN - 0213-2230
DOI - 10.4171/rmi/502
Subject(s) - heisenberg group , travelling salesman problem , group (periodic table) , mathematics , combinatorics , mathematical optimization , computer science , physics , pure mathematics , quantum mechanics
In the Heisenberg group H (endowed with its Carnot-Carathéodory structure), we prove that a compact set E ⊂ H which satisfies an analog of Peter Jones’ geometric lemma is contained in a rectifiable curve. This quantitative condition is given in terms of Heisenberg β numbers which measure how well the set E is approximated by Heisenberg straight lines.
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