So I\'m reading \"Search Through Systematic Set Enumeration\" by Ron Rymon (curr

Question

So I'm reading "Search Through Systematic Set Enumeration" by Ron Rymon (currently available online for free. I'm having a problem with the notation in the following definition presented bellow:

The Set-Enumeration (SE)-tree is a vehicle for representing and/or enumerating sets in a best-first fashion. The complete SE-tree systematically enumerates elements of a power-set using a pre-imposed order on the underlying set of elements. In problems where the search space is a subset of that power-set that is (or can be) closed under set-inclusion, the SE-tree induces a complete irredundant search technique. Let E be the underlying set of elements. We first index E's elements using a one-to-one function ind: E -> N. Then, given any subset S ? E, we define its SE-tree view:

Definition 2.1 A Node's View

View(ind,S)=def{e?E|ind(e)>maxe??Sind(e?)}

In the paper there is an example of a tree made with what appears to be E={1,2,3,4}. I have some familiarity with set-builder notation, but much of the other parts of the "node's view" is confusing me. I skimmed ahead to see if there were clarifications, but I didn't manage to find them so either: a) the author is assuming a competency I do not have, b) the explanation is there and I couldn't find it, or c) the author is doing a horrible job as an author.

So with the hope that it is one of the first two:

I'm assuming that the prime in e' is for the complement of the set e, so if e = {1}, then e' = {2,3,4}. Is this correct?
What is this ind function? What would ind({3,4}) be for example?

maxe??S? Is this the maximum height of the sub tree of the complement of e?

Any assistance on this would be most appreciated.

Explanation / Answer

No, the prime is not complement, e? is just a different variable than e.

In words, View(ind,S) is the set of all edges whose index is higher than the indices of edges in S. The function ind:E?N gives a number to each edge, and maxe??Sind(e?) is simply the highest index of S.

Then View(ind,S) is the set of all edges whose index is higher than maxe??Sind(e?)

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