Querying Temporal and Spatial Constraint Networks in PTIME

M. Koubarakis and S. Skiadopoulos
Artificial Intelligence, 123(1-2):223--263, 2000.

Abstract:
We start with the assumption that temporal and spatial knowledge usually captured by constraint networks can be represented and queried more effectively by using the scheme of indefinite constraint databases. Because query evaluation in this scheme is in general a hard computational problem, we seek tractable instances of query evaluation. We assume that we have a class of constraints C with some reasonable computational and closure properties (the computational properties of interest are that the satisfiability problem and an appropriate version of the variable elimination problem for C should be solvable in PTIME). Under this assumption, we exhibit general classes of indefinite constraint databases and first-order modal queries for which query evaluation can be done with PTIME data complexity. We then search for tractable instances of C among the subclasses of Horn disjunctive linear constraints over the rationals. From previous research we know that the satisfiability problem for Horn disjunctive linear constraints is solvable in PTIME, but not the variable elimination problem. Thus we try to discover subclasses of Horn disjunctive linear constraints with tractable variable elimination problems. The class of UTVPI^{\ne} constraints is the largest class that we show to have this property. Finally, we restate our general tractability results with C ranging over the newly discovered tractable classes. Interesting tractable query answering problems for indefinite temporal and spatial constraint databases are identified in this way. We close our complexity analysis by precisely outlining the frontier between tractable and possibly intractable query answering problems

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