Many real discrete optimization problems (DOPs) are NP -hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special structure using decomposition approaches. An important example of decomposition approaches is tree decomposition with local decomposition algorithms using the special...

Packing and decomposition of combinatorial objects such as graphs, digraphs, and hypergraphs by smaller objects are central problems in combinatorics and combinatorial optimization. Their study combines probabilistic, combinatorial, and algebraic methods. In addition to being among the most fascinating purely combinatorial problems, they are often motivated by algorithmic applications. There ar...

Inspired by decomposition problems in rule-based formalisms in Computational Systems Biology and recent work on compositionality in graph transformation, this paper proposes to use arbitrary colimits to “deconstruct” models of reactions in which states are represented as objects of adhesive categories. The fundamental problem is the decomposition of complex reactions of large states into simple...

This paper introduces the umodules, a generalisation of the notion of module in graph theory. The structure to be decomposed, so-called homogeneous relation, captures among other undirected graphs, tournaments, digraphs, and 2−structures. Our resulting decomposition scheme when restricted to undirected graphs generalises the well-studied modular graph decomposition, and meets the recently intro...

A graph of small branchwidth admits efficient dynamic programming algorithms for many NP-hard problems on the graph. A key step in these algorithms is to find a branch decomposition of small width for the graph. Given a planar graph G of n vertices, an optimal branch decomposition of G can be computed in polynomial time, e.g., by the edge-contraction method in O(n) time. All known algorithms fo...

There is a large class of problems that can be represented by task decomposition trees which specify alternative sets of variables that must be given values. Any one of these alternatives can be represented as a constraint satisfaction problem. We describe a technique for selecting a task decomposition that results in a constraint problem that can be solved efficiently. This technique takes adv...

The structure of real-world complex networks has long been an area of interest, and one common way to describe the structure of a network has been with the k-core decomposition. The core number of a node can be thought of as a measure of its centrality and importance, and is used by applications such as community detection, understanding viral spreads, and detecting fraudsters. However, we obse...

We show how to decompose e ciently in parallel any graph into a number of outerplanar subgraphs called hammocks satisfying certain separator properties Our work combines and extends the sequential hammock decomposition technique intro duced by G Frederickson and the parallel ear decomposition technique thus we call it the hammock on ears decomposition We mention that hammock on ears decomposi...

A decomposition of a graph is a partition of the edge set. One can also look at partitions of the arc set but in this talk we restrict our attention to edges. If each part of the decomposition is a spanning subgraph then we call the decomposition a factorisation and the parts are called factors. Decompositions are especially interesting when the subgraphs induced by each part are pairwise isomo...