# Questions tagged [shortest-path]

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### Combinatorics of Bellman-Ford or how to make cyclic graphs acyclic?

Roughly speaking, my question is: How costly is to make a cyclic graph acyclic while preserving all simple $s$-$t$ paths? Let $K_n$ be a complete undirected graph on vertices $\{0,1,\ldots,n+1\}$. (...
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### Lower bounds on single-source shortest paths in directed graphs

Are there any non-trivial lower bounds on the complexity of single-source shortest paths (SSSP) in a directed graph, where all edges have non-negative edge weights? Can we rule out the possibility of ...
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### Recent progress on the next-to-shortest-path problem for directed graphs?

In the paper "Computing strictly-second shortest paths" (1997), Lalgudi and Papaefthymiou consider the following problem: Let $G$ be a directed graph with edge-weighting $w$. Let $u,v$ be vertices in ...
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### Is APSP verification easier than APSP?

In APSP, the input is an $n$-node directed weighted graph $G$, and the output is an $n \times n$ matrix holding pairwise shortest path distances between nodes in $G$. Define "APSP-Verification" as ...
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### Path finding algorithm to maximise points of interest along the route

I am trying to write an algorithm to find a path (not the shortest one) between a given start and end point. An user will enter the start location, the end location and the available time to travel. ...
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### Dynamic shortest path data structure for DAG

Let $G$ be a dynamic DAG (directed acyclic graph) where new vertices and new edges can be inserted. I am looking for an efficient data structure/algorithm to maintain the shortest path from a fixed ...
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