Related papers: Modified Dijkstra Algorithm with Invention Hierarc…
Indoor navigation systems leverage shortest path algorithms to calculate routes. In order to define the "shortest path", a cost function has to be specified based on theories and heuristics in the application domain. For the domain of…
For the case of evidence ordered in a complete directed acyclic graph this paper presents a new algorithm with lower computational complexity for Dempster's rule than that of step-by-step application of Dempster's rule. In this problem,…
In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…
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…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
Directed Acylic Graphs with a single entry vertex and a single exit vertex (st-DAGs) have many applications. For instance, they are frequently used for modelling flow problems or precedence conditions among tasks, work packages, etc.. This…
We present an implementation and experimental analysis of the deterministic algorithm proposed by Duan et al. (2025) for the Single-Source Shortest Path (SSSP) problem, which achieves the best-known asymptotic upper bound of $O(m \log^{2/3}…
This paper presents a novel multicriteria shortest path search algorithm called Hierarchical MLS. The distinguishing feature of the algorithm is the multilayered structure of compressed k-Path-Cover graphs it operates on. In addition to…
We present new deterministic algorithms for computing distributed weighted minimum weight cycle (MWC) in undirected and directed graphs and distributed weighted all nodes shortest cycle (ANSC) in directed graphs. Our algorithms for these…
Study the general single-source shortest path problem. Firstly, define a path function on a set of some path with same source on a graph, and develop a kind of general single-source shortest path problem (GSSSP) on the defined path…
The algorithms-with-predictions framework has been used extensively to develop online algorithms with improved beyond-worst-case competitive ratios. Recently, there is growing interest in leveraging predictions for designing data structures…
Planning for Autonomous Unmanned Ground Vehicles (AUGV) is still a challenge, especially in difficult, off-road, critical situations. Automatic planning can be used to reach mission objectives, to perform navigation or maneuvers. Most of…
We study the fully dynamic All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. Given an $n$-vertex graph $G$ with non-negative edge lengths, that undergoes an online sequence of edge insertions and deletions, the…
Consider the setting where each vertex of a graph has a function, and communications can only occur between vertices connected by an edge. We wish to minimize the sum of these functions. For the case when each function is the sum of a…
A decentralized search algorithm is a method of routing on a random graph that uses only limited, local, information about the realization of the graph. In some random graph models it is possible to define such algorithms which produce…
We provide a method to obtain beyond-worst-case time complexity for any single-source-shortest-path (SSSP) algorithm by exploiting modular structures in graphs. The key novelty is a graph decomposition, called the acyclic-connected (A-C)…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
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…
Given a weighted digraph D, finding the longest simple path is well known to be NP-hard. Furthermore, even giving an approximation algorithm is known to be NP-hard. In this paper we describe an efficient heuristic algorithm for finding long…