Provably efficient algorithms for resolving temporal and spatial difference constraint violations

A system of difference constraints is a formal model of temporal and spatial constraints in many areas such as scheduling, constraint satisfaction, and layout compaction. During construction of such a system, constraint violations often arise, and they need to be resolved. Previous algorithms for this task fall into two groups: those algorithms that are fast but cannot resolve all violations, and those algorithms that can resolve all violations but are exponentially slow. We propose the first algorithms that are fast as well as able to resolve all violations. Moreover, unlike the previous algorithms, our algorithms support the ordering of violations using their inherent criticality or user-defined priority. We provably and experimentally justify the efficiency and efficacy of our algorithms.

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