Related papers: Optimizing Safe Flow Decompositions in DAGs
Solving the non-convex optimal power flow (OPF) problem for large-scale power distribution systems is computationally expensive. An alternative is to solve the relaxed convex problem or linear approximated problem, but these methods lead to…
Our work concerns algorithms for an unweighted variant of Maximum Flow. In the All-Pairs Connectivity (APC) problem, we are given a graph $G$ on $n$ vertices and $m$ edges, and are tasked with computing the maximum number of edge-disjoint…
We give a deterministic $m^{1+o(1)}$ time algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with $m$ edges and polynomially bounded integral demands, costs, and capacities. As a consequence, we obtain the…
Graph neural networks (GNN) have achieved state-of-the-art performance on various industrial tasks. However, the poor efficiency of GNN inference and frequent Out-Of-Memory (OOM) problem limit the successful application of GNN on edge…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
The massive integration of distributed energy resources changes the operational demands of the electric power distribution system, motivating optimization-based approaches. The added computational complexities of the resulting optimal power…
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…
A semi-streaming algorithm in dynamic graph streams processes any $n$-vertex graph by making one or multiple passes over a stream of insertions and deletions to edges of the graph and using $O(n \cdot \mbox{polylog}(n))$ space.…
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…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
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 provide evidence that computing the maximum flow value between every pair of nodes in a directed graph on $n$ nodes, $m$ edges,and capacities in the range $[1..n]$, which we call the All-Pairs Max-Flow problem, cannot be solved in time…
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 study the vertex-decremental Single-Source Shortest Paths (SSSP) problem: given an undirected graph $G=(V,E)$ with lengths $\ell(e)\geq 1$ on its edges and a source vertex $s$, we need to support (approximate) shortest-path queries in…
Multi-assembly methods rely at their core on a flow decomposition problem, namely, decomposing a weighted graph into weighted paths or walks. However, most results over the past decade have focused on decompositions over directed acyclic…
This paper focuses on an AC optimal power flow (OPF) problem for distribution feeders equipped with controllable distributed energy resources (DERs). We consider a solution method that is based on a continuous approximation of the projected…
We study the maximum flow problem in directed H-minor-free graphs where H can be drawn in the plane with one crossing. If a structural decomposition of the graph as a clique-sum of planar graphs and graphs of constant complexity is given,…
We consider the problem of finding maximum flows in planar graphs with capacities on both vertices and edges and with multiple sources and sinks. We present three algorithms when the capacities are integers. The first algorithm runs in $O(n…
Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing…
We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal non-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a maximal flow…