Related papers: Improving The Floyd-Warshall All Pairs Shortest Pa…
We revisit the problem of finding the shortest path between two selected vertices of a graph and formulate this as an $\ell_1$-regularized regression -- Least Absolute Shrinkage and Selection Operator (lasso). We draw connections between a…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
A straightforward dynamic programming method for the single-source shortest paths problem (SSSP) in an edge-weighted directed acyclic graph (DAG) processes the vertices in a topologically sorted order. First, we similarly iterate this…
Dijkstra's algorithm is one of the most popular classic path planning algorithms, achieving optimal solutions across a wide range of challenging tasks. However, it only calculates the shortest distance from one vertex to another, which is…
We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G=(V,E) with positive edge weights. For this problem we present a decremental algorithm (that…
Images conveniently capture the result of physical processes, representing rich source of information for data driven medicine, engineering, and science. The modeling of an image as a graph allows the application of graph-based algorithms…
Fine-grained reductions have established equivalences between many core problems with $\tilde{O}(n^3)$-time algorithms on $n$-node weighted graphs, such as Shortest Cycle, All-Pairs Shortest Paths (APSP), Radius, Replacement Paths, Second…
Computing shortest paths is one of the most fundamental algorithmic graph problems. It is known since decades that this problem can be solved in near-linear time if all weights are nonnegative. A recent break-through by [Bernstein,…
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…
Cyclic structures are fundamental topological features in graphs, playing critical roles in network robustness, information flow, community structure, and various dynamic processes. Algorithmic tools that can efficiently probe and analyze…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
We present a new pipelined approach to compute all pairs shortest paths (APSP) in a directed graph with nonnegative integer edge weights (including zero weights) in the CONGEST model in the distributed setting. Our deterministic distributed…
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…
We consider the Shortest Odd Path problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum…
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…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
We study the use of machine learning techniques to solve a fundamental shortest path problem, known as the single-source many-targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cycle problem in an undirected n-node graph with edge weights in {1,...,M} or in a…
The shortest path problem is a typical problem in graph theory with wide potential applications. The state-of-the-art single-source shortest paths algorithm on the weight graph is the $\Delta$-stepping algorithm, which can efficiently…