Encoding Class Decision Version of Company Controls

Class Tree
Description Company Controls is a problem in the area of stock market, in which the goal is to determine the pair of companies X,Y such that X controls Y, given information on stock possessions of companies.
We are interested in a decision version of this problem.

Given a situation of shareholdership and a company C, is it true that C is the main controller? In other words, is the number of companies controlled by C greater than or equals to the number of companies controlled by any other company?

Remind that, in order to control a company Y, a company X has to exert control over more than 50% of the stock of Y. Company X can exert control over stock of Y in two different ways: X itself may possess a certain percentage of stock of Y, in this case we say that X directly exerts control over the respective percentage of stock of Y. Alternatively, if X controls a company Z, which exerts control over stock of Y, then we say that X indirectly exerts control over the respective stock of Y. Company then exerts control over the sum of stock of Y over which it directly and indirectly exerts control.

The input is comprised of the company C, the set of all companies and the percentages of directly controlled stock.

More details in

* Inderpal Singh Mumick and Hamid Pirahesh and Raghu Ramakrishnan, "The Magic of Duplicates and Aggregates", Proceedings of the 16th International Conference on Very Large Data Bases (VLDB'90), pp. 264-277.
* David B. Kemp and Peter J. Stuckey, "Semantics of Logic Programs with Aggregates", Proceedings of the International Symposium on Logic Programming (ISLP'91), pp. 387-401.

Input format

The company C is specified by an instance of "checkForMaxControls", for example

checkForMaxControls(c1).

The set of companies is specified by instances of "company", for example

company(c1). company(c2). company(c3). company(c4).

The percentages of directly controlled stock is given by instances of "owns", for example

owns(c1,c2,60). owns(c1,c3,20). owns(c2,c3,40). owns(c3,c4,51).

Output Format

If the number of controlled companies by C is greater than or equals to the number of controlled companies by any other company, the output should be a witness specified by instances of "controls", where controls(x,y) states that company x exerts control on company y. For example, a valid output for the instance above is

controls(c1,c2). controls(c1,c3). controls(c1,c4). controls(c3,c4).

Otherwise, if there is a company exerting control on a number of companies greater than the number of companies controlled by C, the output should be the string "UNSATISFIABLE".

Example

For the input

checkForMaxControls(c1). company(c1). company(c2). company(c3). company(c4). owns(c1,c2,60). owns(c1,c3,20). owns(c2,c3,40). owns(c3,c4,51).

the output should be

controls(c1,c2). controls(c1,c3). controls(c1,c4). controls(c3,c4).

because

* c1 controls 3 companies, that is c2, c3, c4;
* c3 controls only 1 company, that is c4;
* c2 and c4 do not control any company.

Similarly, for

checkForMaxControls(c3). company(c1). company(c2). company(c3). company(c4). owns(c1,c2,60). owns(c1,c3,20). owns(c2,c3,40). owns(c3,c4,51).

the output should be

UNSATISFIABLE

Authors: Mario Alviano
Encodings
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