1. Minimum width color spanning annulus.
- Author
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Acharyya, Ankush, Nandy, Subhas C., and Roy, Sasanka
- Subjects
- *
SET theory , *FIXED point theory , *SPANNING trees , *MATHEMATICAL complex analysis , *ALGORITHMS - Abstract
Given a set P = { p 1 , p 2 , … , p n } of n points in Image 1 and each assigned with one of the given k distinct colors, we study the problem of finding the minimum width color spanning annulus of different shapes. Specifically, we consider the color spanning circular annulus ( C S C A ), axis-parallel square annulus ( C S S A ), axis parallel rectangular annulus ( C S R A ) , and equilateral triangular annulus of fixed orientation ( C S E T A ) . The time complexities of the proposed algorithms for the respective problems are (i) O ( n 3 log n ) for C S C A , (ii) O ( n 3 + n 2 k log k ) for C S S A , (iii) O ( n 4 ) for C S R A , and (iv) O ( n 2 k ) for C S E T A . [ABSTRACT FROM AUTHOR]
- Published
- 2018
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