Search for a minimal set of properties describing a referent in a set of objects

Question

I was wondering if anyone could help me get pointers to solve this problem. A reference to the algorithms would be great, but pointers to documents / information are also good.

The problem is as follows. Suppose I have a set of E entities E={car1, car2, bicycle}and a set of properties P ={red, blue, small}. I also have a knowledge base such that red(bicycle), blue(car1), blue(car2), small(car2). Suppose I also have a referent rwho belongs E.

The task is to find a minimal set of properties P' \subseteq P, so that it uniquely identifies rfrom E. Thus, if r- car2, then P'={small}.

Any ideas? I think that something like the problem of covering a set or functional dependencies (as in DB theory) may give some idea, but I thought I would ask before going into this literature. Another possibility is to build graphs and find algorithms for isomorphisms of subgraphs ... perhaps.

Thanks.

Answer 1

First, find the set of all properties that r has. We call it S. For each property p in S, find e (p), all objects that have property p. For every p from S it is clear that e (p) contains r. Take the intersection e (p) for each p of S. If the intersection contains more than one object, then there is no solution, and we finish the algorithm.

, S , r. S, r. p S, q S, e (p) e (q). , T, e (p) p T - {r}, T . T .

, , , , , , - .

Answer 2

E\{r} () , r ( E).

, NP-.

:

(U, S), U - , , S= {s1, s2,..., sn } - , , :

E= U\union {r}, r - , r U. P= {p1, p2,..., pn} S, E U i , 1 <; = i <= n pi (E), f E si. , r. , , U, r .

, , r, ​​ - r S*, ( U) S*, U ( ). , U , S*.

: U r - E.

, , , NP-.