This post endorses Hodoku’s explanation of strong and weak links, regretfully confined to chains. His discussions of grouping and ALS nodes are supplemented for completeness. Hodoku graphic representation of chains by cell shading and candidate coloring is seen to be unnecessarily obscure, in comparison to Sysudoku ©PowerPoint curve renditions.
After a shaky start, the Hodoku page Chains and Loops settles down as Hodoku defines winks and slinks quite adequately in the section Links and Inferences. Hodoku applies them to chains only, however. In this section chain nodes are candidates and links are defined to be between candidates. The following sections define group nodes and ALS nodes. These are sets of candidates functioning as a node in an AIC. Elsewhere, Hodoku also views cells as seeing each other, a notion criticized in my Paul Stephens review as confusing and unnecessary. If you say that cells see each other when the one candidate in each cell sees the other, what about the other candidates in the cells? The idea confines winks to boxes and lines sharing cells.
Hodoku diagrams pictures groups by cell groups, rather than candidate groups crossing cell boundaries. Groups are marked by shading cells. As convenient as this might be for puzzle graphics, it is inconsistent with chain logic, and makes the definition of a group node awkward. For comparison, see my post Group Theory, where a group is defined as a set of candidates within a unit that is deemed true if it is known that one candidate member is true, and false if all are known to be false.
Hodoku’s graphic representation of groups by cell shading, is not effective. His keypad pencil marking, with no marking of slinks defined by units (houses), makes it worse. To illustrate, compare this Hodoku depiction of a grouped chain . . .
. . . with the Sysudoku version below, which identifies candidate groups, and distinguishes slinks and winks between groups and candidates. The group properties are clear:
Grouped chain segments are X-chain segments.
Grouped line slinks depend on complete alignment..
Grouped slinks depend on the two groups covering all candidates in the unit. Otherwise, any two groups in a unit wink. The true candidate can only be in one of the groups.
With a ©PowerPoint template and a very modest investment in its elements, you can exchange crystal clear renditions of chains and other Sudoku structures with fellow sysudokies. See the tools page. And you can document your progress slide by slide through a difficult puzzle. Just attach the file to an email and send it the whole thing along. You can even send it to me! Sweet revenge for some of my homework challenges.
Hodoku’s account and depiction of the ALS node in an AIC is comparatively obscure as well. Pictures and immediate examples would help. The concept of grouping is key to the ALS node, the groups being ALS candidates of the same number. The internal slink is a group slink, and there is one between each pair of number groups within the ALS. The entering and exit winks must be grouped winks. Did Hodoku cover that? Not in my copy.
For sweet examples, see the Sysudoku post The ALS Node in an AIC , of July 2012.
Next in Chains and Loops, Hodoku illustrates several textual conventions for recording chains. A human solver can’t use these recordings without a picture of the current state of the puzzle.
Although the chain notation doesn’t serve as an explanation of the chain, it does have its uses. A solver can alert another about a chain via email or Twitter, without sending the whole diagram. The text notation is a way for a solver program to report a chain with textual output. Andrew Stuart and others have gone further with that, and programmed the graphic drawing of chains as well. The results don’t tempt me to feed a chain description into a drawing program, but there is curve drawing technology for this.
Besides being obscure, Hodoku graphic renditions of chains have two serious related faults. Most obviously, chain links are represented as arrows, giving an artificial direction to the chain, from its unjustified premise. Secondly, candidates are colored along the chain, reflecting the polarity of the premise. The coloring displays the chain following direction. Chains as objects are bi-directional, as Hobiger knew, but carelessly promoted the opposite. Besides that, candidate coloring is in widespread use as a represention of strong link nets. Bi-colored AIC are in conflict with that.
Next, we look at how Hodoku reports on the various types of chains, as they are encountered in the Sysudoku order of battle. That puts the simplest form of AIC, the XY-chain first, along with its come-along cousin, the remote pair.