Constraint Satisfaction over Shared Multi-set Value Domains

Abstract

Conventional finite-domain constraint satisfaction problems (CSPs), and the algorithms that solve them, assume that: value domains are sets, variable instantiation is constrained only by value, and each variable, or node, has its own value domain. We extend the CSP definition to allow both domains and variable nodes to be multi-sets. By so doing we introduce a type of constraint we call instance- or resource constraints, which are orthogonal to (and may coexist with) conventional value constraints. Our definition further allows for the sharing of domains by multiple nodes, which effectively compete for resources. By allowing multi-sets in domains and in nodes we introduce the following problem: assigning a multi-set of variables $\delta _1 v_1 + ... + \delta _n v_n$ from a multi-set domain $\sigma _1 e_1 + ... + \sigma _m e_m$. This is a permutational search problem.