[PATCH] D59820: [llvm-exegesis] Introduce a 'naive' clustering algorithm (PR40880)

[Clement Courbet via Phabricator via llvm-commits]

courbet added inline comments.


================
Comment at: tools/llvm-exegesis/lib/Clustering.cpp:56
 
+// Given a set of points, checks that all the points are neighbours.
+bool InstructionBenchmarkClustering::areAllNeighbours(
----------------
"are neighbours up to AnalysisClusteringEpsilon"


================
Comment at: tools/llvm-exegesis/lib/Clustering.cpp:57
+// Given a set of points, checks that all the points are neighbours.
+bool InstructionBenchmarkClustering::areAllNeighbours(
+    ArrayRef<size_t> Pts) const {
----------------
This is O(N^2).  You can do it in O(N): compute the cluster centroid (O(N)), then compute distance from each point to centroid (O(N)).

This relies on the fact that if there exists `p` and `q` such that `d(p,q) > e`, then either `d(p, centroid) > e/2` or `d(q, centroid) > e/2.

Proof (ad absurdum):
Assume both `d(p, centroid) <= e/2` and `d(q, centroid) <= e/2`. Then:

```
d(p, centroid)  + d(q, centroid) <= e
```

By symmetry:

```
d(p, centroid)  + d(centroid, q) <= e
```

By [[ https://en.wikipedia.org/wiki/Triangle_inequality#Metric_space | triangle inequality ]]:


```
d (p, q) <= d(p, centroid)  + d(q, centroid) <= e
```





Repository:
  rL LLVM

CHANGES SINCE LAST ACTION
  https://reviews.llvm.org/D59820/new/

https://reviews.llvm.org/D59820