Related papers: Hierarchy construction schemes within the Scale se…
This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of…
A new approach is proposed for finding the "best cut" in a hierarchy of partitions by energy minimization. Said energy must be "climbing" i.e. it must be hierarchically and scale increasing. It encompasses separable energies and those…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
We present a parallel algorithm for computing the minimum s-t cut in structured 3-dimensional proper order graphs arising from image segmentation problems. Proper order graphs are multi-column structures where vertices are arranged in…
Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness…
The assumption of maximum parallelism support for the successful realization of scalable quantum computers has led to homogeneous, ``sea-of-qubits'' architectures. The resulting architectures overcome the primary challenges of reliability…
This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Given points in a domain, a tree structure is first…
Hierarchical structures are ubiquitous in human and animal societies, but a fundamental understanding of their raison d'\^etre has been lacking. Here, we present a general theory in which hierarchies are obtained as the optimal design that…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
Discrete energy minimization is a ubiquitous task in computer vision, yet is NP-hard in most cases. In this work we propose a multiscale framework for coping with the NP-hardness of discrete optimization. Our approach utilizes algebraic…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the…
The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the…
In many manufacturing processes, batch processing is frequently needed for capacity reasons. This applies both to parallel and serial batching. However, while the serial batch processing is largely studied in the literature, as it is…
We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…
We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…
A hierarchical architecture for the optimal management of an ensemble of steam generators is presented. The subsystems are coordinated by a multilayer scheme for jointly sustaining a common load. The high level optimizes the load allocation…
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…