相关论文: Computing persistent homology of directed flag com…
A tower is a sequence of simplicial complexes connected by simplicial maps. We show how to compute a filtration, a sequence of nested simplicial complexes, with the same persistent barcode as the tower. Our approach is based on the coning…
The LCP array is an important tool in stringology, allowing to speed up pattern matching algorithms and enabling compact representations of the suffix tree. Recently, Conte et al. [DCC 2023] and Cotumaccio et al. [SPIRE 2023] extended the…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
Given all pairwise weights (distances) among a set of objects, filtered graphs provide a sparse representation by only keeping an important subset of weights. Such graphs can be passed to graph clustering algorithms to generate hierarchical…
Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
Recent efforts to improve the performance of neural network (NN) accelerators that meet today's application requirements have given rise to a new trend of logic-based NN inference relying on fixed-function combinational logic (FFCL). This…
The use of FPGAs for efficient graph processing has attracted significant interest. Recent memory subsystem upgrades including the introduction of HBM in FPGAs promise to further alleviate memory bottlenecks. However, modern multi-channel…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
Efficient processing and feature extraction of largescale point clouds are important in related computer vision and cyber-physical systems. This work investigates point cloud resampling based on hypergraph signal processing (HGSP) to better…
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Ripser. The cup product operation which is available at…
In cryptographic algorithms, the constants to be multiplied by a variable can be very large due to security requirements. Thus, the hardware complexity of such algorithms heavily depends on the design architecture handling large constants.…
We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation…
We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…
High parallel framework has been proved to be very suitable for graph processing. There are various work to optimize the implementation in FPGAs, a pipeline parallel device. The key to make use of the parallel performance of FPGAs is to…
Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computations. While conventional methods use a number of extra qubits linear in the weight of the syndrome, several improvements have been…
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
The Dowker complex $\mathrm{D}_{R}(X,Y)$ is a simplicial complex capturing the topological interplay between two finite sets $X$ and $Y$ under some relation $R\subseteq X\times Y$. While its definition is asymmetric, the famous Dowker…