Related papers: Non-approximability and Polylogarithmic Approximat…
This paper studies the fundamental problem of how to reroute $k$ unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner and fast. This scheduling…
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…
We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We select one…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
Flow matching (FM) has shown promising results in data-driven planning. However, it inherently lacks formal guarantees for ensuring state and action constraints, whose satisfaction is a fundamental and crucial requirement for the safety and…
Minimum flow decomposition (MFD) -- the problem of finding a minimum set of weighted source-to-sink paths that perfectly decomposes a flow -- is a classical problem in Computer Science, and variants of it are powerful models in different…
In this paper, we derive a number of interesting properties and extensions of the convex flow problem from the perspective of convex geometry. We show that the sets of allowable flows always can be imbued with a downward closure property,…
In this paper we consider generalized flow problems where there is an $m$-edge $n$-node directed graph $G = (V,E)$ and each edge $e \in E$ has a loss factor $\gamma_e >0$ governing whether the flow is increased or decreased as it crosses…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
Network flow interdiction analysis studies by how much the value of a maximum flow in a network can be diminished by removing components of the network constrained to some budget. Although this problem is strongly NP-complete on general…
We present an $m^{4/3+o(1)}\log W$-time algorithm for solving the minimum cost flow problem in graphs with unit capacity, where $W$ is the maximum absolute value of any edge weight. For sparse graphs, this improves over the best known…
We study the maximum $s,t$-flow oracle problem on planar directed graphs where the goal is to design a data structure answering max $s,t$-flow value (or equivalently, min $s,t$-cut value) queries for arbitrary source-target pairs $(s,t)$.…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…
In Bioinformatics, the applications of flow decomposition in directed acyclic graphs are highlighted in RNA Assembly problem. However, it admits multiple solutions where exactly one solution correctly represents the underlying transcripts.…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
The motivation for this work stems from the problem of scheduling requests for flow at supply points along an automated network of open-water channels. The off-take flows are rigid-profile inputs to the system dynamics. In particular, the…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
In this paper, we introduce the solver ConvexFlows for the convex flow problem first defined in the authors' previous work. In this problem, we aim to optimize a concave utility function depending on the flows over a graph. However, unlike…