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More consistent documentation for NP-complete heuristics

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Rangi42
2025-08-18 21:45:26 -04:00
parent b7e0783ae7
commit f7167d8115
2 changed files with 7 additions and 3 deletions
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5
man/rgbgfx.1
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@@ -633,9 +633,10 @@ behavior depends on an internal detail of how the PNG is saved, specifically its
chunk. chunk.
Since few image editors (such as GIMP) expose that detail, this behavior is only kept for compatibility and should be considered deprecated. Since few image editors (such as GIMP) expose that detail, this behavior is only kept for compatibility and should be considered deprecated.
.Pp .Pp
It turns out that palette generation is an NP-complete problem, so It turns out that palette generation is an NP-complete problem known as "pagination", so
.Nm .Nm
does not attempt to find the optimal solution, but instead to find a good one in a reasonable amount of time. does not attempt to find the optimal solution, but instead uses an "overload-and-remove" heuristic to find a good one in a reasonable amount of time.
(There are no guarantees about how this algorithm will generate palettes, apart from the constraints documented above.)
It is possible to compute the optimal solution externally (using a solver, for example), and then provide it to It is possible to compute the optimal solution externally (using a solver, for example), and then provide it to
.Nm .Nm
via via

5
man/rgblink.1
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@@ -193,7 +193,10 @@ option!
.El .El
.Ss Scrambling algorithm .Ss Scrambling algorithm
The default section placement algorithm tries to place sections into as few banks as possible. The default section placement algorithm tries to place sections into as few banks as possible.
(It uses a variation of the "first-fit bin packing" algorithm to do so, although nothing is guaranteed about where it will place any particular section beyond the bank, address, and alignment constraints manually specified for the section.) (It turns out that section placement is an NP-complete problem known as "bin packing", so
.Nm
does not attempt to find the optimal solution, but instead uses a "first-fit" heuristic to find a good one in a reasonable amount of time.
There are no guarantees about where this algorithm will place sections, apart from the bank, address, and alignment constraints manually specified for the sections.)
.Pp .Pp
.Dq Scrambling .Dq Scrambling
instead places sections into a given pool of banks, trying to minimize the number of sections sharing a given bank. instead places sections into a given pool of banks, trying to minimize the number of sections sharing a given bank.