NP-completeness of Partial Chirotope Extendibility
Patrick Baier
TL;DR
This paper demonstrates that determining the extendability of partially defined chirotopes is NP-complete, building on Knuth's earlier proof related to CC-systems, highlighting computational complexity in geometric axiomatizations.
Contribution
It establishes NP-completeness for the partial chirotope extendability problem, extending Knuth's NP-completeness result from CC-systems to chirotopes.
Findings
NP-completeness of partial chirotope extendability
Extension of Knuth's NP-completeness proof to chirotopes
Implications for computational geometry and axiomatizations
Abstract
In the monograph "Axioms and Hulls" (1992) Donald Knuth studies some axiomatizations of geometric situations. The structures described by one of the axiom systems are called CC-systems. Knuth proves that it is NP-complete to decide, whether a partially defined CC-system can be extended to a complete CC-system. The aim of this note is to show that Knuth's proof of this result also implies that it is NP-complete to decide the extendability of partially defined chirotopes.
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Taxonomy
Topicsgraph theory and CDMA systems · semigroups and automata theory · Advanced Combinatorial Mathematics