相关论文: On Near Optimal Spectral Expander Graphs of Fixed …

Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling…

Scenario-based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First-order methods are suitable as they can deal with such large-scale problems, but may fail…

We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…

We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high…

Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…

The rise of accurate machine learning methods for weather forecasting is creating radical new possibilities for modeling the atmosphere. In the time of climate change, having access to high-resolution forecasts from models like these is…

We design new algorithms for approximating 2CSPs on graphs with bounded threshold rank, that is, whose normalized adjacency matrix has few eigenvalues larger than $\varepsilon$, smaller than $-\varepsilon$, or both. Unlike on worst-case…

In this paper, we design sub-linear space streaming algorithms for estimating three fundamental parameters -- maximum independent set, minimum dominating set and maximum matching -- on sparse graph classes, i.e., graphs which satisfy…

Dynamic recommendation, focusing on modeling user preference from historical interactions and providing recommendations on current time, plays a key role in many personalized services. Recent works show that pre-trained dynamic graph neural…

The graph isomorphism problem remains a fundamental challenge in computer science, driving the search for efficient decision algorithms. Due to its ambiguous computational complexity, heuristic approaches such as simulated annealing are…

We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…

We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…

We study the problem of finding large cuts in $d$-regular triangle-free graphs. In prior work, Shearer (1992) gives a randomised algorithm that finds a cut of expected size $(1/2 + 0.177/\sqrt{d})m$, where $m$ is the number of edges. We…

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…

We find new upper bounds on the size of a minimum totally dominating set for random regular graphs and for regular graphs with large girth. These bounds are obtained through the analysis of a local algorithm using a method due to Hoppen and…

State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However,…