# 1-sensitive decremental st-shortest paths (Shortest Path (Directed Graphs))

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## Description

Determine the st-shortest path with a sensitivity of 1 using decremental techniques.

## Related Problems

Generalizations: st-Shortest Path

Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, Second Shortest Simple Path, 1-sensitive (3/2)-approximate ss-shortest paths, 2-sensitive (7/5)-approximate st-shortest paths, 2-sensitive decremental st-shortest paths, Replacement Paths Problem

## Parameters

$V$: number of vertices

$E$: number of edges

$L$: maximum absolute value of edge cost

## Table of Algorithms

Currently no algorithms in our database for the given problem.

## Reductions FROM Problem

Problem | Implication | Year | Citation | Reduction |
---|---|---|---|---|

BMM | assume: BMM then: for directed unweighted graphs with $n$ vertices and $m \geq n$ edges require either $m^{1-o({1})}\sqrt{n}$ preprocessing time or $m^{1-o({1})}/\sqrt{n}$ query time for every function $m$ of $n$ |
2017 | https://arxiv.org/pdf/1703.01638.pdf | link |

Replacement Paths Problem (RPP) | assume: APSP Hypothesis then: target cannot be solved with preprocessing time $O(n^{3-\epsilon})$ and update and query times $O(n^{2-\epsilon})$ for any $\epsilon > {0}$ in directed weighted graphs |
2017 | https://arxiv.org/pdf/1703.01638.pdf | link |