Provan and Billera introduced notions of (weak) decomposability of simplicial complexes as a means of attempting to prove polynomial upper bounds on the diameter of the facet-ridge graph of a simplicial polytope. Recently, De Loera and Klee provided the first examples of simplicial polytopes that are not weakly vertex-decomposable. These polytopes are polar to certain simple transportation poly...

The canonical representation of Boolean functions offered by OBDDs (ordered binary decision diagrams) allows to decide the equivalence of two OBDDs in polynomial time with respect to their size. It is still unknown, if this holds for other more succinct supersets of OBDDs such as FBDDs (free binary decision diagrams) and d-DNNFs (deterministic, decomposable negation normal forms), but it is kno...

A univariate polynomial f over a field is decomposable if it is the composition f = g ◦h of two polynomials g and h whose degree is at least 2. We determine an approximation to the number of decomposable polynomials over a finite field. The tame case, where the field characteristic p does not divide the degree n of f , is reasonably well understood, and we obtain exponentially decreasing error ...

A univariate polynomial f over a field is decomposable if it is the composition f = g ◦h of two polynomials g and h whose degree is at least 2. We determine an approximation to the number of decomposable polynomials over a finite field. The tame case, where the field characteristic p does not divide the degree n of f , is reasonably well understood, and we obtain exponentially decreasing error ...

Provan and Billera defined the notion of weak k-decomposability for pure simplicial complexes in the hopes of bounding the diameter of convex polytopes. They showed the diameter of a weakly k-decomposable simplicial complex ã is bounded above by a polynomial function of the number of k-faces in ã and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of verti...

In this paper we introduce the class of decomposable discrete sets and give a polynomial algorithm for reconstructing discrete sets of this class from four projections. It is also shown that the class of decomposable discrete sets is more general than the class S ′ 8 of hv-convex 8but not 4-connected discrete sets which was studied in [3]. As a consequence we also get that the reconstruction fr...

In this paper we introduce the class of strongly decomposable discrete sets and give an efficient algorithm for reconstructing discrete sets of this class from four projections. It is also shown that every Q-convex set (along the set of directions {x, y}) consisting of several components is strongly decomposable. As a consequence of strong decomposability we get that in a subclass of hv-convex ...

In this article, we deal with graphs modelling interconnection networks of parallel systems (parallel computers, networks of workstations,..). We want to share the nodes of such a network between many users, each one needing a given number of nodes. Thus, a graph G with N vertices is said to be decomposable if for each set fn 1 We show that determining if a given tripode (three disjoint chains ...

We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Köppe, R. Weismantel, A polynomial-time algorithm for optimizing over N-fold 4block decomposable integer programs, Proc. IPCO 2010, Lecture Notes in Computer Science, vol. 6080, Springer, 2...