Re: Help needed: Is Quick-Union-Find the right solution to this problem ?

On Sun, 10 Apr 2005 19:46:32 GMT, aredo3604gif@xxxxxxxxx wrote:

>The user can dynamically enter and change the rule connection between
>objects. The rule is a "<" and so given two objects:
>a < b simply means that b < a can't be set, also it must be a != b.
>And with three objects a < b , b < c means a < c
>
>I studied Quick Union Find algorithms a bit and if I understood them
>correctly, once the user gives the input setting the rules/connection
>between objects, the algorithm will give as output the result of the
>solved connections between objects.
>
>As far as I check on the array or given list of objects from user
>input that it's never added anything like a = b nor b<a when a<b it's
>already in the list, would it work as expected so that I know which
>objects in the list are "the strongest" ones as per user given rules ?
>
>I tried thinking about using simple logic like AND,OR,XOR of compare
>results values but I couldn't find a way to ensure that the
>transitivity rule could be mantained.
>
>So, is a DAG or Quick Union Find the way to go ?
>
>My only concern about Quick Union Find is that it constructs a graph
>with a single highest level root like a tree, right ? But if I am not
>wrong the user could set things in such a way that the graph would
>have more than one "root" .. ?!
>
>Someone please help me to understand what's the right thing I should
>use, and the simpler one that would still let me solve the "which is
>stronger" among the user given objects and user set rules.


After a bit of searching I think that I should use DAG and Topological
Sorting, right ?
Topological sorting on a DAG graph in which the user input can be
checked to avoid reflexive property to be inserted should do the
trick, no ?
Regarding transitivity property to tell the user that a given rule
can't be accepted I have to build up the topological sort list and
check on it everytime, right ?

Or, is there any simpler way to have all of this work without building
up a graph and doing topological sorting on it and so on ?

.

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