Bidirectional replacement paths and k-shortest paths search with dynamic programming
Project description
ShortestPaths
Bidirectional replacement-paths and k-shortest paths search with dynamic programming
requirements |
---|
python3 |
click>=7.1.2 |
networkx>=2.5 |
numpy>=1.19.2 |
matplotlib>=3.3.2 |
Overview
ShortestPaths constitutes thesis source code. It examines the optimization of the bidirectional replacement-paths and k-shortest paths search, using dynamic programming. The algorithm proposed memoizes the states of the search of the parent path and retrieves them upon searching the consequent paths. The optimization was validated experimentally in a parametric analysis of tree parameters, the order, the density and the topology of the graph. The replacement paths problem is solved on both edge-exclusive and node-exlusive variations, as well as both online and offline versions. Regarding the k-shortest paths problem, k online replacement-paths searches are executed, following Yen's algorithm with Lawler's modification, while utilizing the developed bidirectional search with dynamic programming. Dijkstra's algorihtm is used for the shortest path search and a modified Erdős-Rényi random graph model is introduced, controling the density and the topology of the graph. More specifically, the small world property is captured by the topology of the graph, resulting to more realistic representations.
The four supported methods for the k-shortest
paths search are:
- Yen + Dijkstra
- Lawler + Dijkstra
- Lawler + Bid. Dijkstra
- Lawler + Bid. Dijkstra + DP
A PriorityQueue class is implemented as a wrapper around heapq, using the
<priority, entry_counter, entry> triple, as suggested here.
Thesis supervisor: Prof. Kostas Siozios
Install
$ conda install -c mattasa shortestpaths
$ pip install shortestpaths
Usage
$ ksp [OPTIONS] N COMMAND [OPTIONS]
Options:
-k INTEGER number of shortest paths to be generated
[default: 1]
--weighted / --no-weighted [default: True]
--directed
--weights-on [edges|nodes|edges-and-nodes]
[default: edges-and-nodes]
--max-edge-weight INTEGER [default: 1000]
--max-node-weight INTEGER [default: 50]
-y, --yen
-l, --lawler
-b, --bidirectional use bidirectional shortest path search
-p, --parallel use multiprocessing
-d, --dynamic use dynamic programming
-s, --seed INTEGER for random graph
--layout-seed INTEGER fixes the random initialization of the
spirng_layout. [default: 1]
--show-graph plots up to 8 paths
--save-graph format: png
-v, --verbose prints the generated paths
replacement-paths Options:
-f, --failing [edges|nodes] Setting what to fail, path edges or path nodes,
in order to produce the replacement paths.
[default: nodes]
--online When online, the path up until the failure is
kept as it is (the algorithm is getting
informed upon meeting the failed node or edge),
whereas when not online, a new search starts
from the source, ignoring the parent-path (the
algorithm is a priori informed about the
failure).
Examples
$ ksp -v 100
$ ksp --show-graph -k 5 100
$ ksp -v -d -k 20 1000
$ ksp -v --show-graph 200 replacement-paths --failing edges
$ ksp -v --show-graph 200 replacement-paths --failing edges --online
Test
$ pytest --cov=shortestpaths shortestpaths
State retrieval | Replacement-paths offline
State retrieval | Replacement-paths online
License
GNU General Public License v3.0
(C) 2020, Athanasios Mattas
atmattas@physics.auth.gr
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