Related papers: KerGM: Kernelized Graph Matching
We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these…
Graph generation and enumeration problems often require handling equivalent graphs -- those that differ only in vertex labeling. We study how to extend SAT Modulo Symmetries (SMS), a framework for eliminating such redundant graphs, to…
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights…
We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be…
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…
Problems involving multiple networks are prevalent in many scientific and other domains. In particular, network alignment, or the task of identifying corresponding nodes in different networks, has applications across the social and natural…
Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix…
In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first…
Graphons are symmetric measurable functions that arise from a sequence of graphs. A graphon variety is the a set of all graphons defined by a condition of the form $t(g, W) = 0$ for a fixed quantum graph $g$, where $t(.,.)$ is the…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…
The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem (QAP). In this paper, we study the problem from the computational analysis point of view. Several classes of neigborhood structures are…
We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…
We present an entirely new geometric and probabilistic approach to synchronization of correspondences across multiple sets of objects or images. In particular, we present two algorithms: (1) Birkhoff-Riemannian L-BFGS for optimizing the…
Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge…
Quantum compilation requires the development of new algorithms that optimise the cost of implementing quantum computations on physical hardware. Often this gives rise to problems which are asymptotically hard to solve classically, and for…
We consider the problem of counting matchings in planar graphs. While perfect matchings in planar graphs can be counted by a classical polynomial-time algorithm, the problem of counting all matchings (possibly containing unmatched vertices,…