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I have a task in which I must distribute unique resources among consumers. Rules are:

  • each consumer has a set of resource types they can use,
  • each resource is unique,
  • each consumer must receive n>0 resources,
  • all resources must be distributed.

E. g. we have this list of consumers and their preferences:

  • A: {X, W}
  • B: {X, Y, V}
  • C: {X, Z}
  • D: {Z}

We have a list of resources: [X, W, Y, V, Z].

If we assign resources naively by iterating through the list of consumers and providing them with the first available resource from their set, we fail on D because the only Z is already assigned to C. A better solution is this: A(W), B(Y, V), C(X), D(Z).

Looks like a logic programming problem to me! While it is trivial to write a Prolog program that provides solutions for this particular case, what I want is a general program that can solve any such problems, or tell me that no solution for given data exists.

Where should I look, what should I google for, does this problem have a name?

Mischa Arefiev
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1 Answers1

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This is an example of an endless variety of resource allocation tasks for which logic programming is indeed well-suited and frequently used. Related tasks are called transportation and assignment problems in the literature, though the details in this formulation are different. Consider this Prolog formulation as a working starting point with which you can solve such tasks:

distribution([], [], []).
distribution([C-Ps|CPs], Rs0, [C-As|CAs]) :-
        allocation(Ps, As, Rs0, Rs1),
        As = [_|_],
        distribution(CPs, Rs1, CAs).

allocation(_, [], Rs, Rs).
allocation(Ps0, [A|As], Rs0, Rs) :-
        select(A, Ps0, Ps1),
        select(A, Rs0, Rs1),
        allocation(Ps1, As, Rs1, Rs).

distribution/3 expects as its first argument a list of pairs of the form Consumer-Preferences, and as its second argument a list of resources. It relates this instance description to solutions in the form of pairs Consumer-Allocated resources. Example query with SWI-Prolog for the concrete task you specified:

?- distribution([a-[x,w],b-[x,y,v],c-[x,z],d-[z]], [x,w,y,v,z], Ds).
Ds = [a-[w], b-[y, v], c-[x], d-[z]] ;
Ds = [a-[w], b-[v, y], c-[x], d-[z]] ;
false.

You can use this formulation for all tasks of this kind. The formulation is complete: It reports all solutions that exist (and some redundantly, because the allocated resources may be stated in any order, as you already see in the example above; you can introduce symmetry breaking constraints in allocation/4 to avoid this - one way to solve this is to insist that As be ascending with respect to the standard term order), and hence there are no (further) solutions if it answers false.

mat
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