  In planning and scheduling, solving problems with both state and temporal
constraints is hard since these constraints may be highly coupled. Judicious
orderings of events enable solvers to efficiently make decisions over sequences
of actions to satisfy complex hybrid specifications. The ordering problem is
thus fundamental to planning. Promising recent works have explored the ordering
problem as search, incorporating a special tree structure for efficiency.
However, such approaches only reason over partial order specifications. Having
observed that an ordering is inconsistent with respect to underlying
constraints, prior works do not exploit the tree structure to efficiently
generate orderings that resolve the inconsistency. In this paper, we present
Conflict-directed Incremental Total Ordering (CDITO), a conflict-directed
search method to incrementally and systematically generate event total orders
given ordering relations and conflicts returned by sub-solvers. Due to its
ability to reason over conflicts, CDITO is much more efficient than Incremental
Total Ordering. We demonstrate this by benchmarking on temporal network
configuration problems that involve routing network flows and allocating
bandwidth resources over time.
