Minimum-cost flow problem
View article: Minimum flow decomposition in graphs with cycles using integer linear programming
Minimum flow decomposition in graphs with cycles using integer linear programming Open
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 a different f…
View article: Flow-Based Path Planning for Multiple Homogenous UAVs for Outdoor Formation-Flying
Flow-Based Path Planning for Multiple Homogenous UAVs for Outdoor Formation-Flying Open
Collision-free path planning is the most crucial component in multi-UAV formation-flying (MFF). We use unlabeled homogenous quadcopters (UAVs) to demonstrate the use of a flow network to create complete (inter-UAV) collision-free paths. Th…
View article: A $(2+\varepsilon)$-approximation algorithm for the general scheduling problem in quasipolynomial time
A $(2+\varepsilon)$-approximation algorithm for the general scheduling problem in quasipolynomial time Open
We study the general scheduling problem (GSP) which generalizes and unifies several well-studied preemptive single-machine scheduling problems, such as weighted flow time, weighted sum of completion time, and minimizing the total weight of…
View article: A $(2+\varepsilon)$-approximation algorithm for the general scheduling problem in quasipolynomial time
A $(2+\varepsilon)$-approximation algorithm for the general scheduling problem in quasipolynomial time Open
We study the general scheduling problem (GSP) which generalizes and unifies several well-studied preemptive single-machine scheduling problems, such as weighted flow time, weighted sum of completion time, and minimizing the total weight of…
View article: Discounted Cuts: A Stackelberg Approach to Network Disruption
Discounted Cuts: A Stackelberg Approach to Network Disruption Open
We study a Stackelberg variant of the classical Most Vital Links problem, modeled as a one-round adversarial game between an attacker and a defender. The attacker strategically removes up to $k$ edges from a flow network to maximally disru…
View article: Discounted Cuts: A Stackelberg Approach to Network Disruption
Discounted Cuts: A Stackelberg Approach to Network Disruption Open
We study a Stackelberg variant of the classical Most Vital Links problem, modeled as a one-round adversarial game between an attacker and a defender. The attacker strategically removes up to $k$ edges from a flow network to maximally disru…
View article: A Biased Random-Key Genetic Algorithm for Maximum Flow with Minimum Labels
A Biased Random-Key Genetic Algorithm for Maximum Flow with Minimum Labels Open
In this work, we propose a novel Biased Random-Key Genetic Algorithm (BRKGA) to solve the Maximum Flow with Minimum Number of Labels (MF-ML) problem, a challenging NP-Complete variant of the classical Maximum Flow problem defined on graphs…
View article: Stronger Hardness for Maximum Robust Flow and Randomized Network Interdiction
Stronger Hardness for Maximum Robust Flow and Randomized Network Interdiction Open
We study the following fundamental network optimization problem known as Maximum Robust Flow (MRF): A planner determines a flow on $s$-$t$-paths in a given capacitated network. Then, an adversary removes $k$ arcs from the network, interrup…
View article: Acceleration for Distributed Transshipment and Parallel Maximum Flow
Acceleration for Distributed Transshipment and Parallel Maximum Flow Open
We combine several recent advancements to solve $(1+\varepsilon)$-transshipment and $(1+\varepsilon)$-maximum flow with a parallel algorithm with $\tilde{O}(1/\varepsilon)$ depth and $\tilde{O}(m/\varepsilon)$ work. We achieve this by deve…
View article: Stronger Hardness for Maximum Robust Flow and Randomized Network Interdiction
Stronger Hardness for Maximum Robust Flow and Randomized Network Interdiction Open
We study the following fundamental network optimization problem known as Maximum Robust Flow (MRF): A planner determines a flow on $s$-$t$-paths in a given capacitated network. Then, an adversary removes $k$ arcs from the network, interrup…
View article: Acceleration for Distributed Transshipment and Parallel Maximum Flow
Acceleration for Distributed Transshipment and Parallel Maximum Flow Open
We combine several recent advancements to solve $(1+\varepsilon)$-transshipment and $(1+\varepsilon)$-maximum flow with a parallel algorithm with $\tilde{O}(1/\varepsilon)$ depth and $\tilde{O}(m/\varepsilon)$ work. We achieve this by deve…
View article: Efficient Dynamic MaxFlow Computation on GPUs
Efficient Dynamic MaxFlow Computation on GPUs Open
Maxflow is a fundamental problem in graph theory and combinatorial optimisation, used to determine the maximum flow from a source node to a sink node in a flow network. It finds applications in diverse domains, including computer networks,…
View article: Efficient Dynamic MaxFlow Computation on GPUs
Efficient Dynamic MaxFlow Computation on GPUs Open
Maxflow is a fundamental problem in graph theory and combinatorial optimisation, used to determine the maximum flow from a source node to a sink node in a flow network. It finds applications in diverse domains, including computer networks,…
View article: Scalable Maxflow Processing for Dynamic Graphs
Scalable Maxflow Processing for Dynamic Graphs Open
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 exten…
View article: Scalable Maxflow Processing for Dynamic Graphs
Scalable Maxflow Processing for Dynamic Graphs Open
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 exten…
View article: Maximum Flow and Minimum-Cost Flow in Almost-Linear Time
Maximum Flow and Minimum-Cost Flow in Almost-Linear Time Open
We present an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in \(m^{1+o(1)}\) time. Our algorithm builds the flow through…
View article: UNOF 2.0: A Blockchain-Enabled, AI-Driven, and IoT-Optimized Unified Network Optimization Framework for Maximizing Network Flow and Cost Efficiency
UNOF 2.0: A Blockchain-Enabled, AI-Driven, and IoT-Optimized Unified Network Optimization Framework for Maximizing Network Flow and Cost Efficiency Open
Network flow theory encompasses maximal flow problem as a pivotal optimization paradigm, characterized by its broad and diverse range of applications. Existing methodologies for finding maximum flow suffer from limitations including high t…
View article: The Minimum‐Cost Dynamic Flow Problem in a Fixed Graph With a Constant Target Flow Value
The Minimum‐Cost Dynamic Flow Problem in a Fixed Graph With a Constant Target Flow Value Open
A dynamic network is a directed graph where an arc has a capacity and a transit time. A dynamic flow is a flow defined in a dynamic network. We consider the problem of finding a minimum‐cost dynamic flow in a dynamic network where an arc h…
View article: A General Framework for Finding Diverse Solutions via Network Flow and Its Applications
A General Framework for Finding Diverse Solutions via Network Flow and Its Applications Open
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find k solutions that maximize a specified diversity measure - the s…
View article: Minimum Cost Nowhere-Zero Flows and Cut-Balanced Orientations
Minimum Cost Nowhere-Zero Flows and Cut-Balanced Orientations Open
Flows and colorings are disparate concepts in graph algorithms - the former is tractable while the latter is intractable. Tutte [Tutte, 1954; Tutte, 1966] introduced the concept of nowhere-zero flows to unify these two concepts. Jaeger [Ja…
View article: Ticket to Ride: Locally Steered Source Routing for the Lightning Network
Ticket to Ride: Locally Steered Source Routing for the Lightning Network Open
Route discovery in the Lightning Network is challenging because senders observe only static channel capacities while real-time balances remain hidden. Existing locally steered schemes such as SpeedyMurmurs protect path privacy but depend o…
View article: Incremental Approximate Maximum Flow via Residual Graph Sparsification
Incremental Approximate Maximum Flow via Residual Graph Sparsification Open
We give an algorithm that, with high probability, maintains a (1-ε)-approximate s-t maximum flow in undirected, uncapacitated n-vertex graphs undergoing m edge insertions in Õ(m+ n F^*/ε) total update time, where F^{*} is the maximum flow …
View article: A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design
A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design Open
The Multi-Capacity Fixed-Charge Network Flow (MC-FCNF) problem, a generalization of the Fixed-Charge Network Flow problem, aims to assign capacities to edges in a flow network such that a target amount of flow can be hosted at minimum cost…
View article: Near-Optimal Algorithm for Directed Expander Decompositions
Near-Optimal Algorithm for Directed Expander Decompositions Open
In this work, we present the first algorithm to compute expander decompositions in an m-edge directed graph with near-optimal time Õ(m). Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains near-opt…
View article: Cost Optimisation Tool for Multicommodity Network Flow Problem in Telecommunications
Cost Optimisation Tool for Multicommodity Network Flow Problem in Telecommunications Open
In this paper, we consider the problem of minimising the cost of data transmission as a function of the capacity of telecommunication links. To solve this problem, we first formulated a mathematical model, and then we designed and develope…
View article: Almost-Linear Time Algorithms for Incremental Graphs: Cycle Detection, SCCs, s-t Shortest Path, and Minimum-Cost Flow
Almost-Linear Time Algorithms for Incremental Graphs: Cycle Detection, SCCs, s-t Shortest Path, and Minimum-Cost Flow Open
We give the first almost-linear time algorithms for several problems in incremental graphs including cycle detection, strongly connected component maintenance, s-t shortest path, maximum flow, and minimum-cost flow. To solve these problems…
View article: Learning-augmented maximum flow
Learning-augmented maximum flow Open
View article: Applying Quantum Computing to Solve Multicommodity Network Flow Problem
Applying Quantum Computing to Solve Multicommodity Network Flow Problem Open
In this paper, the multicommodity network flow (MCNF) problem is formulated as a mixed integer programing model which is known as NP-hard, aiming to optimize the vehicle routing and minimize the total travel cost. We explore the potential …
View article: High-Accuracy Multicommodity Flows via Iterative Refinement
High-Accuracy Multicommodity Flows via Iterative Refinement Open
The multicommodity flow problem is a classic problem in network flow and combinatorial optimization, with applications in transportation, communication, logistics, and supply chain management, etc. Existing algorithms often focus on low-ac…
View article: On Combinatorial Network Flows Algorithms and Circuit Augmentation for Pseudoflows
On Combinatorial Network Flows Algorithms and Circuit Augmentation for Pseudoflows Open
There is a wealth of combinatorial algorithms for classical min-cost flow problems and their simpler variants like max flow or shortest path problems. It is well-known that many of these algorithms are related to the Simplex method and the…