Related papers: On composition and decomposition operations for ve…
Seymour's decomposition theorem for regular matroids is a fundamental result with a number of combinatorial and algorithmic applications. In this work we demonstrate how this theorem can be used in the design of parameterized algorithms on…
Recently, we have introduced and modified two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product…
In this work we study a linear operator $f$ on a pre-euclidean space $\mathcal{V}$ by using properties of a corresponding graph. Given a basis $\B$ of $\mathcal{V}$, we present a decomposition of $\mathcal{V}$ as an orthogonal direct sum of…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
Vector quantization(VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution presents a theoretical foundation of…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
Recently, we have introduced two graph-decomposition theorems based on a new graph product (the vertex-removing synchronised product (VRSP)), motivated by applications in the context of synchronising periodic real-time processes. In these…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
Given $n$ subspaces of a finite-dimensional vector space over a fixed finite field $\mathbb F$, we wish to find a "branch-decomposition" of these subspaces of width at most $k$ that is a subcubic tree $T$ with $n$ leaves mapped bijectively…
Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are often subject to constraints, ruling out many candidates for composed rules. Focusing on the case of…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in $d$-space into constant-complexity subcells. In this paper, we settle in the affirmative a few long-standing open…
If V(R) is the vertex set of a symmetric cycle R in the tope graph of a simple oriented matroid M, then for any tope T of M there exists a unique inclusion-minimal subset Q(T,R) of V(R) such that T is the sum of the topes of Q(T,R). If for…
We prove a robust contraction decomposition theorem for $H$-minor-free graphs, which states that given an $H$-minor-free graph $G$ and an integer $p$, one can partition in polynomial time the vertices of $G$ into $p$ sets $Z_1,\dots,Z_p$…
All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rational Pythagorean hodograph curves. We study vector subspaces…
Let $A$ be a, not necessarily closed, linear relation in a Hilbert space $\sH$ with a multivalued part $\mul A$. An operator $B$ in $\sH$ with $\ran B\perp\mul A^{**}$ is said to be an operator part of $A$ when $A=B \hplus (\{0\}\times \mul…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
We introduce a graph decomposition which exists for all simple, connected graphs $G=(V,E)$. The decomposition $V = A \cup B \cup C$ is such that each vertex in $A$ has more neighbors in $B$ than in $A$ and vice versa. $C$ is `balanced':…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…