Related papers: Hyperfinite graphings and combinatorial optimizati…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
A fundamental problem in pattern avoidance is describing the asymptotic behavior of the extremal function and its generalizations. We prove an equivalence between the asymptotics of the graph extremal function for a class of bipartite…
The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…
We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
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…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this…
We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…
Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…
We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
Recently, connections have been explored between the complexity of finite problems in graph theory and the complexity of their infinite counterparts. As is shown in our paper (and in independent work of Tirza Hirst and D. Harel from a…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…