Related papers: New Solutions to the Firing Squad Synchronization …
Efficiently solving large-scale linear systems is a critical challenge in electromagnetic simulations, particularly when using the Crank-Nicolson Finite-Difference Time-Domain (CN-FDTD) method. Existing iterative solvers are commonly…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their…
We study four systems and their interactions. First, we formulate a unified system of coupled forward-backward stochastic partial differential equations (FB-SPDEs) with Levy jumps, whose drift, diffusion, and jump coefficients may involve…
Many large-scale scientific computations require eigenvalue solvers in a scaling regime where efficiency is limited by data movement. We introduce a parallel algorithm for computing the eigenvalues of a dense symmetric matrix, which…
Parallel physical information neural networks (P-PINNs) have been widely used to solve systems with multiple coupled physical fields, such as the coupled Stokes-Darcy equations with Beavers-Joseph-Saffman (BJS) interface conditions.…
All traditional methods of computing shortest paths depend upon edge-relaxation where the cost of reaching a vertex from a source vertex is possibly decreased if that edge is used. We introduce a method which maintains lower bounds as well…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
Adaptive traffic signal control (ATSC) can effectively reduce vehicle travel times by dynamically adjusting signal timings but poses a critical challenge in real-world scenarios due to the complexity of real-time decision-making in dynamic…
We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared…
We present a parallel solver for numerical constraint satisfaction problems (NCSPs) that can scale on a number of cores. Our proposed method runs worker solvers on the available cores and simultaneously the workers cooperate for the search…
The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs $\varepsilon \subseteq E$ or vertices $\nu \subseteq V$ whose removal $G\setminus \varepsilon$, $G\setminus \nu$…
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
The discontinuous Galerkin (DG) method is widely being used to solve hyperbolic partial differential equations (PDEs) due to its ability to provide high-order accurate solutions in complex geometries, capture discontinuities, and exhibit…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to a…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture…
Spiking Neural Networks (SNNs) are extensively utilized in brain-inspired computing and neuroscience research. To enhance the speed and energy efficiency of SNNs, several many-core accelerators have been developed. However, maintaining the…
Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the…