Related papers: Universal Optimality of Dijkstra via Beyond-Worst-…
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…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
All traditional methods of computing shortest paths depend upon edge-relaxation where the cost of reaching a vertex from a source vertex is possibly decreased if that edge is used. We introduce a method which maintains lower bounds as well…
Using Dijkstra's algorithm to compute the shortest paths in a graph from a single source node to all other nodes is common practice in industry and academia. Although the original description of the algorithm advises using a Fibonacci Heap…
The single-source shortest path problem is a classical problem in the research field of graph algorithm. In this paper, a new single-source shortest path algorithm for nonnegative weight graph is proposed. The algorithm can compress…
A heap is a dynamic data structure that stores a set of labeled values under the following operations: pop returns the minimum value of the heap, Push($x_i$) pushes a new value $x_i$ onto the heap, and DecreaseKey($i$, $v$) decreases the…
This paper describes the shortest path problem in weighted graphs and examines the differences in efficiency that occur when using Dijkstra's algorithm with a Fibonacci heap, binary heap, and self-balancing binary tree. Using C++…
Although Dijkstra's algorithm has near-optimal time complexity for the problem of finding a shortest path from a given vertex $s$ to a given vertex $t$, in practice other algorithms are often superior on huge graphs. A prominent example is…
We present the generic Dijkstra shortest path algorithm: an efficient algorithm for finding a shortest path in an optical network, both in a wavelength-division multiplexed network, and an elastic optical network (EON). The proposed…
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…
Dijkstra's algorithm is the standard method for computing shortest paths on arbitrary graphs. However, it is slow for large graphs, taking at least linear time. It has been long known that for real world road networks, creating a hierarchy…
The Dijkstra algorithm is a classic path planning method, which in a discrete graph space, can start from a specified source node and find the shortest path between the source node and all other nodes in the graph. However, to the best of…
The recently-proposed generic Dijkstra algorithm finds shortest paths in networks with continuous and contiguous resources. While the algorithm was proposed in the context of optical networks (and is applicable to other networks with finite…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
A modified version of the Dijkstra algorithm using an inventive contraction hierarchy is proposed. The algorithm considers a directed acyclic graph with a conical or semi-circular structure for which a pair of edges is chosen iteratively…
Generic Dijkstra is a novel algorithm for finding the optimal shortest path in both wavelength-division multiplexed networks (WDM) and elastic optical networks (EON), claimed to outperform known algorithms considerably. Because of its…
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…
In theoretical computer science, it is a common practice to show existential lower bounds for problems, meaning there is a family of pathological inputs on which no algorithm can do better. However, most inputs of interest can be solved…
Recently we submitted a paper, whose title is A New Fast Unweighted All-pairs Shortest Path Search Algorithm Based on Pruning by Shortest Path Trees, to arXiv. This is related to unweighted graphs. This paper also presents a new fast…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…