clusterlin: include topological pot subsets automatically (optimization)

Automatically add topologically-valid subsets of the potential set pot
to inc. It can be proven that these must be part of the best reachable
topologically-valid set from that work item.

This is a crucial optimization that (apparently) reduces the maximum
number of iterations from ~2^(N-1) to ~sqrt(2^N).

Co-Authored-By: Suhas Daftuar <sdaftuar@gmail.com>

src/test/fuzz/cluster_linearize.cpp

@@ -553,6 +553,12 @@ FUZZ_TARGET(clusterlin_search_finder)
         // longer connected after removing certain transactions, this holds, because the connected
         // components are searched separately.
         assert(iterations_done <= (uint64_t{1} << (todo.Count() - 1)));
+        // Additionally, test that no more than sqrt(2^N)+1 iterations are required. This is just
+        // an empirical bound that seems to hold, without proof. Still, add a test for it so we
+        // can learn about counterexamples if they exist.
+        if (iterations_done >= 1 && todo.Count() <= 63) {
+            Assume((iterations_done - 1) * (iterations_done - 1) <= uint64_t{1} << todo.Count());
+        }
 
         // Perform quality checks only if SearchCandidateFinder claims an optimal result.
         if (iterations_done < max_iterations) {
@@ -769,6 +775,13 @@ FUZZ_TARGET(clusterlin_linearize)
     if (n <= 19 && iter_count > (uint64_t{1} << n)) {
         assert(optimal);
     }
+    // Additionally, if the assumption of sqrt(2^k)+1 iterations per step holds, the maximum number
+    // of iterations is also bounded by (2 + sqrt(2)) * (sqrt(2^n) - 1) + n, which is less than
+    // (2 + sqrt(2)) * sqrt(2^n) + n. Subtracting n and squaring gives
+    // (6 + 4 * sqrt(2)) * 2^n < 12 * 2^n.
+    if (n <= 35 && iter_count > n && (iter_count - n) * (iter_count - n) >= uint64_t{12} << n) {
+        Assume(optimal);
+    }
 
     // If Linearize claims optimal result, run quality tests.
     if (optimal) {