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By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
Among the many possible approaches for the parallelization of self-organizing networks, and in particular of growing self-organizing networks, perhaps the most common one is producing an optimized, parallel implementation of the standard…
We present faster approximation algorithms for generalized network flow problems. A generalized flow is one in which the flow out of an edge differs from the flow into the edge by a constant factor. We limit ourselves to the lossy case,…
We propose a novel penalty method framework for the non-self-adjoint topology optimization problems, taking compliant mechanism problems as an example, by incorporating a convex nonlocal perimeter approximation scheme. We rigorously analyze…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…
Optimal power flow (OPF) has been used for real-time grid operations. Prior efforts demonstrated that utilizing flexibility from dynamic topologies will improve grid efficiency. However, this will convert the linear OPF into a mixed-integer…
In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub…
The Maximum Flow (Max-Flow) problem is a cornerstone in graph theory and combinatorial optimization, aiming to determine the largest possible flow from a designated source node to a sink node within a capacitated flow network. It has…
Fueled by algorithmic advances, AI algorithms are increasingly being deployed in settings subject to unanticipated challenges with complex social effects. Motivated by real-world deployment of AI driven, social-network based suicide…
We demonstrate the relevance of an algorithm called generalized iterative scaling (GIS) or simultaneous multiplicative algebraic reconstruction technique (SMART) and its rescaled block-iterative version (RBI-SMART) in the field of optimal…
In this study, we investigate the performance of two novel first-order optimization algorithms, namely the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF). These algorithms are derived from the forward Euler discretization…
This paper deals with the trade-off between time, workload, and versatility in self-stabilization, a general and lightweight fault-tolerant concept in distributed computing.In this context, we propose a transformer that provides an…
We present a new algorithm to quickly generate high-performance GPU implementations of complex imaging and vision pipelines, directly from high-level Halide algorithm code. It is fully automatic, requiring no schedule templates or…
This paper introduces GODDeS: a fully distributed self-organizing decision-theoretic routing algorithm designed to effectively exploit high quality paths in lossy ad-hoc wireless environments, typically with a large number of nodes. The…
Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that…
The graph isomorphism (GI) problem is the computational problem of finding a permutation of vertices of a given graph $G_1$ that transforms $G_1$ to another given graph $G_2$ and preserves the adjacency. In this work, we propose a quantum…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
Establishing dense correspondences between a pair of images is an important and general problem, covering geometric matching, optical flow and semantic correspondences. While these applications share fundamental challenges, such as large…