Related papers: Chain complex reduction via fast digraph traversal
We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
We study the widely used hierarchical agglomerative clustering (HAC) algorithm on edge-weighted graphs. We define an algorithmic framework for hierarchical agglomerative graph clustering that provides the first efficient $\tilde{O}(m)$ time…
A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering…
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…
Discrete Morse theory has emerged as a powerful tool for a wide range of problems, including the computation of (persistent) homology. In this context, discrete Morse theory is used to reduce the problem of computing a topological invariant…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
A family of comparison-based exact pattern matching algorithms is described. They utilize multi-dimensional arrays in order to process more than one adjacent text window in each iteration of the search cycle. This approach leads to a lower…
Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
Time series often appear in an additive hierarchical structure. In such cases, time series on higher levels are the sums of their subordinate time series. This hierarchical structure places a natural constraint on forecasts. However,…
Multi-robot path planning is difficult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of…
Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…
The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…
State-of-the-art parallel sorting algorithms for distributed-memory architectures are based on computing a balanced partitioning via sampling and histogramming. By finding samples that partition the sorted keys into evenly-sized chunks,…