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TCSPs (Temporal Constraint Satisfaction Problems), as defined in [Dechter etal., 1991], get rid of unary constraints by binarizing them after having addedan "origin of the world" variable. In this work, we look at the constraintsbetween the "origin of the world" variable and the other variables, as the(binarized) domains of these other variables. With this in mind, we define anotion of arc-consistency for TCSPs, which we will refer to asbinarized-domains Arc-Consistency, or bdArc-Consistency for short. We providean algorithm achieving bdArc-Consistency for a TCSP, which we will refer to asbdAC-3, for it is an adaptation of Mackworth's [1977] well-knownarc-consistency algorithm AC-3. We show that if a convex TCSP, referred to in[Dechter et al., 1991] as an STP (Simple Temporal Problem), isbdArc-Consistent, and its "origin of the world" variable disconnected from noneof the other variables, its binarized domains are minimal. We provide twopolynomial backtrack-free procedures: one for the task of getting, from abdArc-Consistent STP, either that it is inconsistent or, in case ofconsistency, a bdArc-Consistent STP refinement whose "origin of the world"variable is disconnected from none of the other variables; the other for thetask of getting a solution from a bdArc-Consistent STP whose "origin of theworld" variable is disconnected from none of the other variables. We then showhow to use our results both in a general TCSP solver and in a TCSP-based jobshop scheduler. From our work can be extracted a one-to-all all-to-one shortestpaths algorithm of an IR-labelled directed graph. Finally, we show that anexisting adaptation to TCSPs of Mackworth's [1977] path-consistency algorithmPC-2 is not guaranteed to always terminate, and correct it.

A binarized-domains arc-consistency algorithm for TCSPs: its  computational analysis and its use as a filtering procedure in solution  search algorithms