Quite correct, the textual output is pretty obscure. I've just released a version which I hope improves this. For example, now says

Killer Cage Splitting
All the cages entirely inside columns 1,2 add up to 70. The cage starting on C1 can be split into an Innie (4 cells that sum to 20) and an Outie (2 cells that sum to 12). The new cages have combinations that mean...
we an remove 1/2/6 from A3
we an remove 1/2/6 from A4

Hi, your very welcome! Thanks for the feedback

Interesting question.

Killers require the cages and the clue numbers. The grid, the box shapes and the size is assumed. In the early days I noticed a lot of definitions tried to use cage boundaries but this is overly complex. For me, it is sufficient to have a 'mapping color' (the classic 4 color mapping problem) and a cage boundary is merely where adjacency has two different colors. The mapping color algorithm is most visible in the cage drawing popup (see "Enter New Killer") but it very basic - I allow a fifth color if necessary (A sixth is available but I've never seen it). Internally cages are numbered so I can uniquely identify them and create more (cage splitting strategy eg) and the numbering could be used instead of the mapping color but the mapping color only requires one digit.

Clues are assumed to be placed in the top leftmost cell of any cage. The solver will barf if they are not. This leaves a lot of zeros. A string of numbers delimited by commas would be shorter but harder to debug/read manually. So the 'standard' email link I employ is 81+162 characters of data:

Click on this link:
http://www.sudokuwiki.org/killersudoku.htm?bd=1121222121221131321333231332314244442414122222
41333132233112131111322131224344431,14002117140000030700000000001
4052200001900001200000000270018150016000000000500000126000000000
0001300002219000011001000150000120900000700000000001300030015000
00000

Now, there is huge scope for compressing this but I haven’t researched it - something I've been meaning to do. I have noticed that some email systems refuse to turn this into a hyper link that includes all the data, which is annoying - and that’s the only reason I'd want to compress it.

I should also get on and do the import popup but I'm not sure how anyone else stores their killers electronically. Sudoku definitions abound (and are easy to import) but killer needs two different strings as input. I've assumed most people will be 'importing' through a link like the one above.

Small mistake in your chain, easily done, but you are working with the correct idea.
-5[h3] +5[j1]
In this case you can't turn off -5[h3] AND then ON +5[j1] because there is another 5 in H1. When you turn OFF and make a strong link there must be only two candidates left in the unit or cell. Weak links where you turn ON obliterates all other candidates in every direction from two upwards.

Hope that helps

Very well observed and yes there was a bug in the output string. Took me all day to track down because a) the code is a few years old now in those parts and b) we are dealing with a cage that had been split, so the original 21 clue over 5 cells wasn’t being used but the pseudo cage of 10 over 3 cells. What also throw me was the solver was splitting the cage even though there were no eliminations to be done - and then moving on to the next strategy, which is okay, since normally a split cage will make things easier. I have now added the word "split" to "cage" if it is a split cage.

I've also improved the text returned on cage combinations. I also spotted another bug where the last remaining cell in a cage wasn't being returned. A Bit of a howler that as it’s an easy thing to compute and a human would fill it doing it on pen a and pencil. But it is now showing on the solver. The check was in my offline solver which is probably why I didn't spot it before.

Solvers all say version 1.94 now, so refresh a few times if you don’t see that.

Cheers Chris, kind words thank you. Killer solver still lags behind Sudoku solver somewhat but I've been given some good hints by various people. I'll keep chipping away at it, you can be sure.

Share and enjoy

Very glad the website is working for you, have fun!

I split the combinations strategy into two parts because one is much easier than another - in most cases. The 'easy' is where a cage has only one combination. From that it will be fairly obvious what candidates can be pruned. The 'hard' is where several combinations are possible and its more work to work out what can be removed just from the combinations. The solver does take into account what remains so easy and hard are not fixed. However, if you are half way through a puzzle lots of other eliminations may make a so-called hard relatively easy to work out, combination wise. I was thinking in terms of how a human would approach a puzzle and they, I assume, would want to pick off the easy combination cages first.

The XOR on the groups of strategies is by design but I can't remember why I did it like that : )

I do not know, to be honest. That’s a difficult combinatorics problem. For a jigsaw shape pattern to be 'nice' I prefer never to use cages that approximate a row or column, ie more than 7 cells in a line. That removes a large number. To still be Sudoku the shapes shouldn't map onto existing constraints. Reflection, rotation and other symmetries multiply the total number of 'unique' patterns.