Related papers: Convex Network Flows
Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
The aim of this paper is to develop a general framework for training neural networks (NNs) in a distributed environment, where training data is partitioned over a set of agents that communicate with each other through a sparse, possibly…
Collaborative edge computing addresses the resource constraints of individual edge nodes by enabling resource sharing and task co-processing across multiple nodes. To fully leverage the advantages of collaborative edge computing, joint…
In the current era of neural networks and big data, higher dimensional data is processed for automation of different application areas. Graphs represent a complex data organization in which dependencies between more than one object or…
We propose a hidden convexity-based method to address distributed optimal energy flow (OEF) problems for transmission-level integrated electricity-gas systems. First, we develop a node-wise decoupling method to de-compose an OEF problem…
This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first algorithmic framework for the minimization of the sum of a smooth nonconvex…
To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…
In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to…
We study hard constraint satisfaction problems with a decimation approach based on message passing algorithms. Decimation induces a renormalization flow in the space of problems, and we exploit the fact that this flow transforms some of the…
We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs,…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
We study distributed network flows as solvers in continuous time for the linear algebraic equation $\mathbf{z}=\mathbf{H}\mathbf{y}$. Each node $i$ has access to a row $\mathbf{h}_i^{\rm T}$ of the matrix $\mathbf{H}$ and the corresponding…
FiniteFlow is a public framework for defining and executing numerical algorithms over finite fields and reconstructing multivariate rational functions. The framework allows to build complex algorithms by combining basic building blocks into…
The terminal backup problems (Anshelevich and Karagiozova (2011)) form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to find a minimum cost subgraph satisfying the connectivity…
Convex optimization is a powerful tool for resource allocation and signal processing in wireless networks. As the network density is expected to drastically increase in order to accommodate the exponentially growing mobile data traffic,…
We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…
Convex relaxations and approximations of the optimal power flow (OPF) problem have gained significant research and industrial interest for planning and operations in electric power networks. One approach for reducing their solve times is…