Timeline for Generating uniquely $k$-optimal point sets
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| May 1, 2020 at 7:20 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title (the question was bumped anyway)
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| May 16, 2017 at 18:02 | history | edited | Manfred Weis | CC BY-SA 3.0 |
added a link to a definition of k-optimality
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| May 16, 2017 at 17:54 | comment | added | Manfred Weis | @Wolfgang you put I right; I should have written "some simple polygons are $2$-optimal" because geometric intersection of a pair of non-adjacent edges requires the adjacent points to be in convex configuration. | |
| May 16, 2017 at 15:03 | comment | added | Wolfgang | OK, almost what I thought then. (modulo $k$ vs. $k+1$) So to get it straight: Joseph O'Rourke's 2nd tour is 1-optimal (if it doesn't matter that the orientation of the short edge in the circuit has changed), the 3rd one is 2-optimal. | |
| May 16, 2017 at 14:56 | comment | added | Manfred Weis | 2@Wolfgang a tour is $k$-optimal, iff it can't be improved by exchanging $k$ or fewer edges or, put differently: any better tour has at least $k+1$ different edges. Simple polygons are $2$-optimal, but polygons with intersecting pairs of non-adjacent edges are $1$-optimal because they can be improved by exchanging a pair of crossing edges. I think the term "$k$-optimal was coined by Lin and/or Kernighan, but I have to look that up. | |
| May 16, 2017 at 12:19 | comment | added | Wolfgang | You have never defined k-optimal. Do you mean a tour which is not optimal but can be improved by exchanging k edges, while exchanging fewer than k edges can never improve it? | |
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| Feb 20, 2016 at 12:50 | history | edited | Manfred Weis | CC BY-SA 3.0 |
reverted previous change of definition of $k$-optimal tour in response to Joseph O'Rourke's answer
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| Feb 20, 2016 at 11:55 | answer | added | Joseph O'Rourke | timeline score: 0 | |
| Feb 20, 2016 at 10:56 | history | edited | Manfred Weis | CC BY-SA 3.0 |
corrected the charakterization of uniqueness of k-optimality; no improvement possible if at least k edges are exchanged (and not k or fewer).
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| Feb 20, 2016 at 9:59 | history | asked | Manfred Weis | CC BY-SA 3.0 |