Related papers: Extended Dijkstra algorithm and Moore-Bellman-Ford…
The disjoint paths problem is a fundamental problem in algorithmic graph theory and combinatorial optimization. For a given graph $G$ and a set of $k$ pairs of terminals in $G$, it asks for the existence of $k$ vertex-disjoint paths…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
We present two new algorithms for solving the {\em All Pairs Shortest Paths} (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves the APSP problem for weighted…
The present work extends the randomized shortest-paths framework (RSP), interpolating between shortest-path and random-walk routing in a network, in three directions. First, it shows how to deal with equality constraints on a subset of…
Physarum solver, also called the physarum polycephalum inspired algorithm (PPA), is a newly developed bio-inspired algorithm that has an inherent ability to find the shortest path in a given graph. Recent research has proposed methods to…
Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path…
The well-known $k$-disjoint path problem ($k$-DPP) asks for pairwise vertex-disjoint paths between $k$ specified pairs of vertices $(s_i, t_i)$ in a given graph, if they exist. The decision version of the shortest $k$-DPP asks for the…
We present a shared memory implementation of a parallel algorithm, called delta-stepping, for solving the single source shortest path problem for directed and undirected graphs. In order to reduce synchronization costs we make some…
The Floyd-Warshall algorithm is the most popular algorithm for determining the shortest paths between all pairs in a graph. It is very a simple and an elegant algorithm. However, if the graph does not contain any negative weighted edge,…
Let G be a weighted (directed) graph with n vertices and m edges. Given a source vertex s, Dijkstra's algorithm computes the shortest path lengths from s to all other vertices in O(m + n log n) time. This bound is known to be worst-case…
We consider the single-source shortest paths problem on a directed graph with real-valued (possibly negative) edge weights and solve this problem in $n^{2+o(1)}$ time by refining the shortcutting procedure introduced in Li, Li, Rao, and…
The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick…
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…
We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
Many applications require minimizing a family of optimization problems indexed by some hyperparameter $\lambda \in \Lambda$ to obtain an entire solution path. Traditional approaches proceed by discretizing $\Lambda$ and solving a series of…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
We present an optimal and efficient algorithm for finding a shortest path in an elastic optical network. The algorithm is an adaptation of the Dijkstra shortest path algorithm, where we take into account the spectrum continuity and…
Shortest path computation is a fundamental problem in road networks. However, in many real-world scenarios, determining solely the shortest path is not enough. In this paper, we study the problem of finding k-Dissimilar Paths with Minimum…
Exact computation of shortest paths in weighted graphs has been traditionally studied in one of two settings. First, one can assume that the edge weights are real numbers and all the performed operations on reals (typically comparisons and…
In this paper we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is…