vn/first: multi-criteria support

Author: hhirtz

src/algorithms/vn/first.rs

@@ -29,18 +29,20 @@ where
     let (min_load, mut max_load) = part_loads.iter().cloned().minmax().into_option().unwrap();
     let mut imbalance = max_load.clone() - min_load;
 
-    let mut i = weights.len();
+    let mut i = 0;
     let mut i_last = 0;
     let mut algo_iterations = 0;
-    while i != i_last {
-        i = (i + 1) % weights.len();
-
+    loop {
         // loop through the weights.
         let p = partition[i];
 
         if part_loads[p] < max_load {
             // weight #i is not in the heaviest partition, and thus the move
             // will not reduce the max imbalance.
+            i = (i + 1) % weights.len();
+            if i == i_last {
+                break;
+            }
             continue;
         }
 
@@ -56,129 +58,23 @@ where
             let (new_min_load, new_max_load) =
                 part_loads.iter().cloned().minmax().into_option().unwrap();
             let new_imbalance = new_max_load.clone() - new_min_load.clone();
-            if imbalance < new_imbalance {
+            if new_imbalance <= imbalance {
+                // The move decreases the partition imbalance.
+                imbalance = new_imbalance;
+                max_load = new_max_load;
+                partition[i] = q;
+                i_last = i;
+            } else {
                 // The move does not decrease the partition imbalance.
                 part_loads[p] += weights[i].clone();
                 part_loads[q] = part_loads[p].clone() - weights[i].clone();
                 continue;
             }
-            imbalance = new_imbalance;
-            max_load = new_max_load;
-            partition[i] = q;
-            i_last = i;
-        }
-
-        algo_iterations += 1;
-    }
-
-    algo_iterations
-}
-
-#[allow(dead_code)]
-pub fn vn_first<const C: usize, T>(
-    partition: &mut [usize],
-    criteria: &[[T; C]],
-    num_parts: usize,
-) -> usize
-where
-    T: AddAssign + SubAssign + Sub<Output = T> + Sum,
-    T: Zero + One + FromPrimitive,
-    T: Copy + Ord,
-{
-    if num_parts < 2 || criteria.is_empty() || C == 0 {
-        return 0;
-    }
-
-    assert_eq!(criteria.len(), partition.len());
-
-    let mut part_loads_per_criterion = {
-        let mut loads = vec![[T::zero(); C]; num_parts];
-        for (w, weight) in criteria.iter().enumerate() {
-            for (part_load, criterion) in loads[partition[w]].iter_mut().zip(weight) {
-                *part_load += *criterion;
-            }
-        }
-        loads
-    };
-    let total_weight_per_criterion = {
-        // TODO replace with .collect() once [_; C] implements FromIterator.
-        let mut ws = [T::zero(); C];
-        for c in 0..C {
-            ws[c] = part_loads_per_criterion[c].iter().cloned().sum();
-        }
-        ws
-    };
-    if total_weight_per_criterion.contains(&T::zero()) {
-        return 0;
-    }
-
-    let min_max_loads = |part_loads_per_criterion: &Vec<[T; C]>| -> [(T, T); C] {
-        // TODO replace with .collect() once [_; C] implements FromIterator.
-        let mut imbs = [(T::zero(), T::zero()); C];
-        for c in 0..C {
-            imbs[c] = part_loads_per_criterion[c]
-                .iter()
-                .cloned()
-                .minmax()
-                .into_option()
-                .unwrap();
         }
-        imbs
-    };
-
-    let (global_min_load, mut global_max_load) = *min_max_loads(&part_loads_per_criterion)
-        .iter()
-        .max_by_key(|(min_load, max_load)| *max_load - *min_load)
-        .unwrap();
-    let mut imbalance = global_max_load - global_min_load;
 
-    let mut i = 0;
-    let mut i_last = 0;
-    let mut algo_iterations = 0;
-    while i != i_last {
-        i = (i + 1) % criteria.len();
-
-        // loop through the weights.
-        let p = partition[i];
-
-        if part_loads_per_criterion[p]
-            .iter()
-            .all(|criterion_load| *criterion_load < global_max_load)
-        {
-            // weight #i is not in the heaviest partition, and thus the move
-            // will not reduce the max imbalance.
-            continue;
-        }
-
-        for q in 0..num_parts {
-            // loop through the parts.
-            if p == q {
-                // weight #i is already in partition #q.
-                continue;
-            }
-
-            for c in 0..C {
-                part_loads_per_criterion[p][c] -= criteria[i][c];
-                part_loads_per_criterion[q][c] += criteria[i][c];
-            }
-            let (new_global_min_load, new_global_max_load) =
-                *min_max_loads(&part_loads_per_criterion)
-                    .iter()
-                    .max_by_key(|(min_load, max_load)| *max_load - *min_load)
-                    .unwrap();
-            let new_imbalance = new_global_max_load - new_global_min_load;
-            if imbalance < new_imbalance {
-                // The move does not decrease the partition imbalance.
-                for c in 0..C {
-                    part_loads_per_criterion[p][c] += criteria[i][c];
-                    part_loads_per_criterion[q][c] -= criteria[i][c];
-                }
-                continue;
-            }
-            imbalance = new_imbalance;
-            global_max_load = new_global_max_load;
-            partition[i] = q;
-            i_last = i;
+        i = (i + 1) % weights.len();
+        if i == i_last {
+            break;
         }
 
         algo_iterations += 1;
@@ -280,18 +176,26 @@ mod tests {
     #[test]
     fn small() {
         const W: [[i32; 2]; 6] = [[1, 2], [2, 4], [3, 6], [8, 4], [10, 5], [12, 6]];
-        let mut part = [0; W.len()];
+        let w: Vec<_> = W
+            .iter()
+            .map(|w| nalgebra::SVector::<i32, 2>::from(*w))
+            .collect();
+        let mut partition = [0; W.len()];
 
-        vn_first(&mut part, &W, 1);
+        vn_first_mono(&mut partition, &w, 2);
+        println!("partition: {partition:?}");
         let imbs_ini: Vec<i32> = (0..W[0].len())
-            .map(|c| imbalance::max_imbalance(2, &part, W.iter().map(|w| w[c])))
+            .map(|c| imbalance::max_imbalance(2, &partition, W.iter().map(|w| w[c])))
+            .collect();
+        vn_first_mono(&mut partition, &w, 2);
+        println!("partition: {partition:?}");
+        let imbs_end: Vec<i32> = (0..W[0].len())
+            .map(|c| imbalance::max_imbalance(2, &partition, W.iter().map(|w| w[c])))
             .collect();
-        vn_first(&mut part, &W, 2);
-        let imbs_end =
-            (0..W[0].len()).map(|c| imbalance::max_imbalance(2, &part, W.iter().map(|w| w[c])));
+        println!("imbalances: {imbs_end:?} < {imbs_ini:?}");
         for (imb_ini, imb_end) in imbs_ini.into_iter().zip(imbs_end) {
+            println!("imbalance: {imb_end} < {imb_ini}");
             assert!(imb_end <= imb_ini);
-            println!("imbalance : {} < {}", imb_end, imb_ini);
         }
     }
 
@@ -303,7 +207,7 @@ mod tests {
             (weights, mut partition) in
                 (2..200_usize).prop_flat_map(|num_weights| {
                     let weights = prop::collection::vec(
-                        (1..1000_i32, 1..1000_i32).prop_map(|(a, b)| [a, b]),
+                        (1..1000_i32, 1..1000_i32).prop_map(|(a, b)| nalgebra::SVector::<i32, 2>::new(a, b)),
                         num_weights
                     );
                     let partition = prop::collection::vec(0..1_usize, num_weights);
@@ -313,7 +217,7 @@ mod tests {
             let imbs_ini: Vec<i32> = (0..C)
                 .map(|c| imbalance::max_imbalance(2, &partition, weights.iter().map(|w| w[c])))
                 .collect();
-            vn_first(&mut partition, &weights, 2);
+            vn_first_mono(&mut partition, &weights, 2);
             let imbs_end: Vec<i32> = (0..C)
                 .map(|c| imbalance::max_imbalance(2, &partition, weights.iter().map(|w| w[c])))
                 .collect();