Related papers: Electrical Flows over Spanning Trees
We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…
We present a conceptually clear and algorithmically useful framework for parameterizing the costs of tensor network contraction. Our framework is completely general, applying to tensor networks with arbitrary bond dimensions, open legs, and…
AC optimal power flow (AC OPF) is a fundamental problem in power system operation and control. Accurately modeling the network physics via the AC power flow equations makes AC OPF a challenging nonconvex problem that results in significant…
Given a graph $G$ and a digraph $D$ whose vertices are the edges of $G$, we investigate the problem of finding a spanning tree of $G$ that satisfies the constraints imposed by $D$. The restrictions to add an edge in the tree depend on its…
We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We show the…
A spanning tree $T$ of graph $G$ is a $\rho$-approximate universal Steiner tree (UST) for root vertex $r$ if, for any subset of vertices $S$ containing $r$, the cost of the minimal subgraph of $T$ connecting $S$ is within a $\rho$ factor of…
In the spanning tree congestion problem, given a connected graph $G$, the objective is to compute a spanning tree $T$ in $G$ that minimizes its maximum edge congestion, where the congestion of an edge $e$ of $T$ is the number of edges in…
Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a…
This paper proposes a convex optimization based method that either locates all real roots of a set of power flow equations or declares no real solution exists in the given area. In the proposed method, solving the power flow equations is…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Network connectedness is indispensable for the normal operation of transmission networks. However, there still remains a lack of efficient constraints that can be directly added to the problem formulation of optimal transmission switching…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
We tackle the problem of goal-directed graph construction: given a starting graph, a budget of modifications, and a global objective function, the aim is to find a set of edges whose addition to the graph achieves the maximum improvement in…
We develop a new algorithmic framework for designing approximation algorithms for cut-based optimization problems on capacitated undirected graphs that undergo edge insertions and deletions. Specifically, our framework dynamically maintains…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…
Given an unweighted tree $T=(V,E)$ with terminals $K \subset V$, we show how to obtain a $2$-quality vertex flow and cut sparsifier $H$ with $V_H = K$. We prove that our result is essentially tight by providing a $2-o(1)$ lower-bound on the…
We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network…
The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly,…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
This paper studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e.,…