update README with new approx algorithm and metrics

1 files changed, 7 insertions, 3 deletions

diff --git a/README.md b/README.md
index fd38eab..29997ae 100644
--- a/README.md
+++ b/README.md
@@ -8,19 +8,23 @@ The sorting can be accessed by letting the progam print the image paths in order
 Detailed usage:
 
 ```
-embeddings-sort [OPTIONS] [IMAGES]...
+Usage: embeddings-sort [OPTIONS] [IMAGES]...
 
 Arguments:
   [IMAGES]...  
 
 Options:
-  -e, --embedder <EMBEDDER>        Characteristic to sort by [default: content] [possible values: brightness, hue, color, content]
+  -e, --embedder <EMBEDDER>        Characteristic to sort by [default: content-euclidean] [possible values: brightness, hue, color, content-euclidean, content-angular-distance, content-manhatten]
   -s, --symlink-dir <SYMLINK_DIR>  Symlink the sorted images into this directory
   -o, --copy-dir <COPY_DIR>        Copy the sorted images into this directory. Uses COW when available
   -c, --stdout                     Write sorted paths into stdout, one per line
   -0, --stdout0                    Write sorted paths into stdout, null-separated. Overrides -c
+  -b, --benchmark                  Output total tour length to stderr
+      --tsp-approx <TSP_APPROX>    Algorithm for TSP approximation. Leave as default if unsure [default: christofides] [possible values: mst-dfs, christofides, christofides-refined]
   -h, --help                       Print help
 ```
 
 ## Insides
-The TSP approximation is done by using Prim's algorithm and doing a DFS through the resulting MST, giving a 2-approximation, which gives ok-ish results, but could be improved by using something like Christofides algorithm and doing attempts at improving the initial approximation. This is O(n²) time, however even for 10k images this should still be much quicker than the embedding step. The embeddings are therefore cached, usually in `$HOME/.cache/embeddings-sort`.
+The chrisofides implementation uses an approximated min-weight matching algorithm, which may be non-ideal, though I haven't benchmarked how much of a difference it makes (mainly due to the implementation complexity of an exact algorithm, which would also increase the implementations complexity from O(n²) to O(n³) where n is the number of given images).
+
+christofides-refined is planned to be christofides but with an O(n²) 2-opt-swapping step added after the main algorithm. Implementing this efficiently will also require some algorithmic trickery, so it's not ready yet.