Minimum size tree-decompositions

Minimum Size Tree-decompositions

We study in this paper the problem of computing a tree-decomposition of a graph with width at most k and minimum number of bags. More precisely, we focus on the following problem: given a fixed k ≥ 1, what is the complexity of computing a treedecomposition of width at most k with minimum number of bags in the class of graphs with treewidth at most k? We prove that the problem is NP-complete for...

Size-Constrained Tree Decompositions

Tree-Decompositions are the corner-stone of many dynamic programming algorithms for solving graph problems. Since the complexity of such algorithms generally depends exponentially on the width (size of the bags) of the decomposition, much work has been devoted to compute tree-decompositions with small width. However, practical algorithms computing tree-decompositions only exist for graphs with ...

Minimum feature size preserving decompositions

The minimum feature size of a crossing-free straight line drawing is the minimum distance between a vertex and a non-incident edge. This quantity measures the resolution needed to display a figure or the tool size needed to mill the figure. The spread is the ratio of the diameter to the minimum feature size. While many algorithms (particularly in meshing) depend on the spread of the input, none...

Minimum tree decompositions with a given tree as a factor

Bounding Search Space Size via (Hyper)tree Decompositions

This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to exploit determinism in the problem specification and produce tighter bounds. We demonstrate on a variety of practical problem instances that we are often able to ...