This paper introduces the umodules, a generalisation of modules for the homogeneous relations. We first present some properties of the umodule family, then show that, if the homogeneous relation fulfills some natural axioms, the umodule family has a unique decomposition tree. We show that this tree can be computed in polynomial time, under a certain size assumption. We apply this theory to a ne...

This paper introduces the umodules, a generalisation of modules for the homogeneous relations. We first present some properties of the umodule family, then show that, if the homogeneous relation fulfills some natural axioms, the umodule family has a unique decomposition tree. We show that this tree can be computed in polynomial time, under a certain size assumption. We apply this theory to a ne...

A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation princi...

Wediscuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable, that is, whether it can be partitioned into connected parts of orders α1, α2, . . . , αk for every α1, α2, . . . , αk summing up to the order of the graph. In contrast, we show that the decision problem...

Let S = {K1,3,K3, P4} be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph G into graphs taken from any non-empty S′ ⊆ S. The problem is known to be NP-complete for any possible choice of S′ in general graphs. In this paper, we assume that the input graph is cubic, and study the computational complexity of the problem of partitioning its edge se...

A new method of model registration is proposed using graphical templates. A graph of landmarks is chosen in the template image. All possible candidates for these landmarks are found in the data image using local operators. A dynamic programming algorithm on decomposable subgraphs of the template graph finds the optimal match to a subset of the candidate points in polynomial time. This combinati...

Let F be a non-zero polynomial with integer coefficients in N variables of degree M . We prove the existence of an integral point of small height at which F does not vanish. Our basic bound depends on N and M only. We separately investigate the case when F is decomposable into a product of linear forms, and provide a more sophisticated bound. We also relate this problem to a certain extension o...

This diploma thesis is concerned with functional decomposition f = g ◦ h of polynomials. First an algorithm is described which computes decompositions in polynomial time. This algorithm was originally proposed by Zippel (1991). A bound for the number of minimal collisions is derived. Finally a proof of a conjecture in von zur Gathen, Giesbrecht & Ziegler (2010) is given, which states a classifi...

The L-decomposable and the bi-decomposable models are two families of distributions on the set Sn of all permutations of the first n positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these...

We consider the problem of recovering an orthogonally decomposable tensor with a subset elements distorted by noise arbitrarily large magnitude. focus on particular case where each mode in decomposition is corrupted vectors components that are correlated locally, i.e., nearby components. show this deterministic completion has unusual property it can be solved polynomial time if rank sufficientl...