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| * Input Predicates: produced_by/5, controlled_by/5 * Query Predicate: query/2 * Output Predicates: strategic/1 |
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| C = c_1, ..., c_m | C = c_1, ..., c_m |
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| - Companies in C' produce all goods in $G$; | - Companies in C' produce all goods in G; <<BR>> |
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| - If O_i is a subset of C', the associated company c_i must belong to C'(for each i=1,...,m$. | - If O_i is a subset of C', the associated company c_i must belong to C'(for each i=1,...,m). <<BR>> |
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| 1. each product is produced by at most four companies; and | 1. each product is produced by at most four companies; and <<BR>> |
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| 2. each company is controlled by at most four companies. | 2. each company is controlled by at most four companies. <<BR>> |
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| Under these restrictions the problem is still NP^NP-complete. Instances of strategic companies are encoded by means of the predicates produced_by and controlled_by. In particular, there is a fact producedBy(p,c1,c2,c3,c4) when a product p is produced by companies c1, c2, c3 and c4, and a fact controlledBy(c,c1,c2,c3,c4) when a company c is controlled by companies c1, c2, c3 and c4. If a product p is produced by less than four companies (but at least one), the atom produced_by(p,c_a,c_b,c_c,c_d) contains repetitions of companies. For instance, producedBy(p,c_a,c_b,c_c,c_c) is used for representing that p is produced solely by c_a, c_b and c_c. Analogously, if a company c is controlled by less than four companies. |
Under these restrictions the problem is still NP^NP-complete. <<BR>> Instances of strategic companies are encoded by means of the predicates produced_by and controlled_by. In particular, there is a fact {{{producedBy(p,c1,c2,c3,c4)}}} when a product p is produced by companies c1, c2, c3 and c4, and a fact {{{controlledBy(c,c1,c2,c3,c4)}}} when a company c is controlled by companies c1, c2, c3 and c4. If a product p is produced by less than four companies (but at least one), the atom {{{produced_by(p,c_a,c_b,c_c,c_d)}}} contains repetitions of companies. For instance, {{{producedBy(p,c_a,c_b,c_c,c_c)}}} is used for representing that p is produced solely by c_a, c_b and c_c. Analogously, if a company c is controlled by less than four companies. |
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== Predicates == * '''Input''': {{{produced_by/5, controlled_by/5}}} * '''Query''': {{{query/2}}} * '''Output''': {{{strategic/1}}} |
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| - A set of facts of the form produced_by(p,c1,c2,c3,c4), where produced_by(p,c1,c2,c3,c4) means that product P is produced by companies c1, c2, c3 and c4; | - A set of facts of the form {{{produced_by(p,c1,c2,c3,c4)}}}, where {{{produced_by(p,c1,c2,c3,c4)}}} means that product P is produced by companies c1, c2, c3 and c4; |
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| - A set of facts of the form controlled_by(c,c1,c2,c3,c4), where controlled_by(c,c1,c2,c3,c4) means that company c is jointly controlled by c1, c2, c3 and c4; | - A set of facts of the form {{{controlled_by(c,c1,c2,c3,c4)}}}, where {{{controlled_by(c,c1,c2,c3,c4)}}} means that company c is jointly controlled by c1, c2, c3 and c4; |
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| - A ground query atom of the form query(c1,c2), specifying the query goal: Do c1 and c2 belong to a (minimal) strategic set? |
- A ground query atom of the form {{{query(c1,c2)}}}, specifying the query goal: Do c1 and c2 belong to a (minimal) strategic set? |
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| If the answer to the input query is positive (i.e., for query(c1,c2), c1 and c2 jointly belong to a minimal strategic set), the output must contain a number of ground atoms of the form strategic(i) (where "strategic(i)" stands for "company i is strategic") witnessing that c1 and c2 belong to a strategic set. | If the answer to the input query is positive (i.e., for query(c1,c2), c1 and c2 jointly belong to a minimal strategic set), the output must contain a number of ground atoms of the form {{{strategic(i)}}} (where "strategic(i)" stands for "company i is strategic") witnessing that c1 and c2 belong to a strategic set. |
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| * Affiliation: | * Affiliation: University of Genova |
Strategic Companies
Contents
Problem Description
Strategic companies is a well-known NP^NP-complete problem that has often been used for systems comparisons, and also in the previous ASP Competitions.
In the Strategic Companies problem, a collection
- C = c_1, ..., c_m
of companies is given, for some m>=1. Each company produces some goods in a set G, and each company c_i in C is possibly controlled by a set of owner companies O_i (where O_i is a subset of C, for each i=1,...,m). In this context, a set C' of companies (i.e., a subset of C) is a "strategic set" if it is minimal among all the sets satisfying the following conditions:
- Companies in C' produce all goods in G;
- If O_i is a subset of C', the associated company c_i must belong to C'(for each i=1,...,m).
In our setting, instances are subjected to two additional restrictions:
each product is produced by at most four companies; and
each company is controlled by at most four companies.
Under these restrictions the problem is still NP^NP-complete.
Instances of strategic companies are encoded by means of the predicates produced_by and controlled_by. In particular, there is a fact producedBy(p,c1,c2,c3,c4) when a product p is produced by companies c1, c2, c3 and c4, and a fact controlledBy(c,c1,c2,c3,c4) when a company c is controlled by companies c1, c2, c3 and c4. If a product p is produced by less than four companies (but at least one), the atom produced_by(p,c_a,c_b,c_c,c_d) contains repetitions of companies. For instance, producedBy(p,c_a,c_b,c_c,c_c) is used for representing that p is produced solely by c_a, c_b and c_c. Analogously, if a company c is controlled by less than four companies.
Moreover, two distinct companies c_i,c_j in C are provided in input (by means of predicate query), and the existence of a strategic set C' such that c_i and c_j occur in C' has to be checked.
Predicates
Input: produced_by/5, controlled_by/5
Query: query/2
Output: strategic/1
Input format
An instance of STRATCOMP is modeled by the following facts that will be provided in the input file:
- A set of facts of the form produced_by(p,c1,c2,c3,c4), where produced_by(p,c1,c2,c3,c4) means that product P is produced by companies c1, c2, c3 and c4;
- A set of facts of the form controlled_by(c,c1,c2,c3,c4), where controlled_by(c,c1,c2,c3,c4) means that company c is jointly controlled by c1, c2, c3 and c4;
- A ground query atom of the form query(c1,c2), specifying the query goal: Do c1 and c2 belong to a (minimal) strategic set?
For instance:
produced_by(pasta,barilla,amato,dececco,divella). produced_by(tonno,callipo,star,almera,asdomar). controlled_by(callipo,star,almera,asdomar,barilla). controlled_by(barilla,callipo,almera,dececco,star). query(callipo,barilla)?
Output format
If the answer to the input query is positive (i.e., for query(c1,c2), c1 and c2 jointly belong to a minimal strategic set), the output must contain a number of ground atoms of the form strategic(i) (where "strategic(i)" stands for "company i is strategic") witnessing that c1 and c2 belong to a strategic set.
Example
Author(s)
- Author: Mario Alviano
- Affiliation: University of Calabria, Italy
- Author: Marco Maratea
- Affiliation: University of Genova
- Author: Francesco Ricca
- Affiliation: University of Calabria, Italy