The Complexity of Bicriteria Tree-Depth

The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph G. We introduce bicriteria generalization in which additionally the width needs to bounded by some integer b. are interested case when G is line tree, proving that \(\mathcal {NP}\)-hard and obtaining polynomial-time additive 2b-approximation algorithm. This particular class graphs received significant attention, mainly due potential applications. These include purely combinatorial applications like searching tree-like partial orders (which generalizes binary search sorted data), or practical ones parallel processing.