Related papers: Chain complex reduction via fast digraph traversal
Homomorphic encryption (HE) enables computation over encrypted data but incurs a substantial overhead. For sparse-matrix vector multiplication, the widely used Halevi and Shoup (2014) scheme has a cost linear in the number of occupied…
Subgraph matching is a compute-intensive problem that asks to enumerate all the isomorphic embeddings of a query graph within a data graph. This problem is generally solved with backtracking, which recursively evolves every possible partial…
In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
A novel method to obtain hierarchical and overlapping clusters from network data -i.e., a set of nodes endowed with pairwise dissimilarities- is presented. The introduced method is hierarchical in the sense that it outputs a nested…
We present Agglomerative Token Clustering (ATC), a novel token merging method that consistently outperforms previous token merging and pruning methods across image classification, image synthesis, and object detection & segmentation tasks.…
A fundamental question that shrouds the emergence of massively parallel computing (MPC) platforms is how can the additional power of the MPC paradigm be leveraged to achieve faster algorithms compared to classical parallel models such as…
One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation…
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by…
For an even integer t \geq 2, the Matchings Connecivity matrix H_t is a matrix that has rows and columns both labeled by all perfect matchings of the complete graph K_t on t vertices; an entry H_t[M_1,M_2] is 1 if M_1\cup M_2 is a…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…
Counting the number of perfect matchings in bipartite graphs, or equivalently computing the permanent of 0-1 matrices, is an important combinatorial problem that has been extensively studied by theoreticians and practitioners alike. The…
A matching cut is a matching that is also an edge cut. In the problem Minimum Matching Cut, we ask for a matching cut with the minimum number of edges in the matching. We investigate the differences in complexity between Minimum Matching…
Analog layout synthesis requires some elements in the circuit netlist to be matched and placed symmetrically. However, the set of symmetries is very circuit-specific and a versatile algorithm, applicable to a broad variety of circuits, has…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
The Minimum Quartet Tree Cost problem is to construct an optimal weight tree from the $3{n \choose 4}$ weighted quartet topologies on $n$ objects, where optimality means that the summed weight of the embedded quartet topologies is optimal…
The multiplication of a matrix by its transpose, $A^T A$, appears as an intermediate operation in the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm (ATA) for computing this product, based upon…
The Morse-Smale complex is a standard tool in visual data analysis. The classic definition is based on a continuous view of the gradient of a scalar function where its zeros are the critical points. These points are connected via gradient…