Obstructions for bounded shrub-depth and rank-depth

Tree-depth of Graphs: Characterisations and Obstructions

Depth-bounded Discrepancy Search

Many search trees are impractical ly large to explore exhaustively. Recently, techniques like l imi ted discrepancy search have been proposed for improving the chance of f inding a goal in a l imi ted amount of search. Depth-bounded discrepancy search offers such a hope. The motivat ion behind depth-bounded discrepancy search is that branching heuristics are more likely to be wrong at the top o...

Depth - bounded Discrepancy

Many search trees are impractically large to explore exhaustively. Recently, techniques like limited discrepancy search have been proposed for improving the chance of nding a goal in a limited amount of search. Depth-bounded discrepancy search ooers such a hope. The motivation behind depth-bounded discrepancy search is that branching heuristics are more likely to be wrong at the top of the tree...

Bounded Depth Data Trees

A data tree is a tree where each node has a label from a finite set, and a data value from a possibly infinite set. We consider data trees whose depth is bounded beforehand. By developing an appropriate automaton model, we show that under this assumption various formalisms, including a two variable first-order logic and a subset of XPath, have decidable emptiness problems.

Shrub-depth: Capturing Height of Dense Graphs

The recent increase of interest in the graph invariant called tree-depth and in its applications in algorithms and logic on graphs led to a natural question: is there an analogously useful “depth” notion also for dense graphs (say; one which is stable under graph complementation)? To this end we introduced, in a 2012 conference paper, the notion of shrub-depth of a graph class which is related ...