Dijkstra's algorithm - Wikipedia
en.wikipedia.org › wiki › Dijkstra&The Dijkstra algorithm uses labels that are positive integers or real numbers, which are totally ordered. It can be generalized to use any labels that are partially ordered, provided the subsequent labels (a subsequent label is produced when traversing an edge) are monotonically non-decreasing.
Lecture 13: Dijkstra’s Algorithm - MIT OpenCourseWare
ocw.mit.edu › courses › 6-006-introduction-to• Claim: At end of Dijkstra’s algorithm, d(s, v) = δ(s, v) for all v ∈ V • Proof: – If relaxation sets d(s, v) to δ(s, v), then d(s, v) = δ(s, v) at the end of the algorithm ∗ Relaxation can only decrease estimates d(s, v) ∗ Relaxation is safe, i.e., maintains that each d(s, v) is weight of a path to v (or ∞)
A Novel All-Pairs Shortest Path Algorithm - arxiv.org
arxiv.org › pdf › 2208algorithm, and Matrix algorithm, which are the typical algo-rithms for solving the shortest path problems. 2.1 Dijkstra’s algorithm Dijkstra et al. proposed and solved two graph problems: con-structing the tree of minimum total length between nodes, and finding the path of minimum total length between two given nodes, and [13]. The main ...