The topological complexity of the ordered configuration space of disks in a strip
Year: 2024
Type: article
Abstract: How hard is it to program n n robots to move about a long narrow aisle such that only w w of them can fit across the width of the aisle? In this paper, we answer that question by calculating the topological complexity of conf ( n , w ) \operatorname {conf}(n,w) , the ordered configuration space of n n open unit-diameter disks in the infinite strip of width w w . By studying its cohomology ring, we prove that, as long as n n is greater than w w , the topological complexity of conf ( n , w ) \operatorname {conf}(n,w) is 2 n − 2 ⌈ n w ⌉ + 1 2n-2\big \lceil \frac {n}{w}\big \rceil +1 , providing a lower bound for the minimum number of cases such a program must consider.
DOI: 10.1090/bproc/246
Author: Nicholas Wawrykow
Institution: University of Chicago
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $750
OpenAlex ID: W4405272985