Related papers: Maximum capacity path problem with loss factors
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the…
We give an $O(n^{1.5} \log n)$ algorithm that, given a directed planar graph with arc capacities, a set of source nodes and a set of sink nodes, finds a maximum flow from the sources to the sinks.
We study the unsplittable flow on a path problem (UFP) where we are given a path with non-negative edge capacities and tasks, which are characterized by a subpath, a demand, and a profit. The goal is to find the most profitable subset of…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
With the tremendous increase of the Internet traffic, achieving the best performance with limited resources is becoming an extremely urgent problem. In order to address this concern, in this paper, we build an optimization problem which…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
This paper deals with the problem of computing, in an online fashion, a maximum benefit multi-commodity flow (\ONMCF), where the flow demands may be bigger than the edge capacities of the network. We present an online, deterministic,…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to fast, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity…
Research on container loading problems has been proved effective in increasing the filling rate of containers in different practical situations. However, the broader logistic context might pressure the loading process, leading to…
We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…
We extend the well known bottleneck paths problem in two directions for directed unweighted (unit edge cost) graphs with positive real edge capacities. Firstly we narrow the problem domain and compute the bottleneck of the entire network in…
In this paper, we develop an online method that leverages machine learning to obtain feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps on extremely fast timescales (e.g., milliseconds), bypassing…
The problem of finding an electric vehicle route that optimizes both driving time and energy consumption can be modeled as a bicriterion path problem. Unfortunately, the problem of finding optimal bicriterion paths is NP-complete. This…
We present an algorithm for computing $s$-$t$ maximum flows in directed graphs in $\widetilde{O}(m^{4/3+o(1)}U^{1/3})$ time. Our algorithm is inspired by potential reduction interior point methods for linear programming. Instead of using…
Computing routing schemes that support both high throughput and low latency is one of the core challenges of network optimization. Such routes can be formalized as $h$-length flows which are defined as flows whose flow paths are restricted…