Related papers: Partial order approach to compute shortest paths i…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is…
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…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a "travel time" value, are…
It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a…
We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
This paper proposes a generalised framework for density estimation in large networks with measurable spatiotemporal variance in edge weights. We solve the stochastic shortest path problem for a large network by estimating the density of the…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
We study the NP-hard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices $s$ and $t$, the goal is to delete as…
We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…
A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to…
This paper outlines the ideas behind developing a graph-based heuristic-driven routing algorithm designed for a particular instance of a goods transportation problem with a single good type. The proposed algorithm solves the optimization…
Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide…
We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…