[SYSTEMML-2025] Improved codegen optimizer (search space layout)

This patch makes a minor improvement to the codegen optimizer. So far we
linearized the search space by sorting cutsets by their scores and
appending all other interesting points. Now, we sort the remaining
interesting points decreasing according to their size, which can improve
the pruning efficiency by skipping larger sub spaces.

src/main/java/org/apache/sysml/hops/codegen/opt/ReachabilityGraph.java

@@ -69,7 +69,9 @@ public ReachabilityGraph(PlanPartition part, CPlanMemoTable memo) {
 		//short-cut for partitions without cutsets
 		if( tmpCS.isEmpty() ) {
 			_cutSets = new CutSet[0];
-			_searchSpace = part.getMatPointsExt();
+			//sort materialization points in decreasing order of their sizes
+			//which can improve the pruning efficiency by skipping larger sub-spaces.
+			_searchSpace = sortBySize(part.getMatPointsExt(), memo, false);
 			return;
 		}
 
@@ -120,15 +122,17 @@ else if( current.get(0).equals(node) )
 				.map(p -> p.getLeft()).toArray(CutSet[]::new);
 
 		//created sorted order of materialization points
-		//(cut sets in predetermined order, all other points appended)
+		//(cut sets in predetermined order, other points sorted by size)
 		HashMap<InterestingPoint, Integer> probe = new HashMap<>();
 		ArrayList<InterestingPoint> lsearchSpace = new ArrayList<>();
 		for( CutSet cs : _cutSets ) {
 			CollectionUtils.addAll(lsearchSpace, cs.cut);
 			for( InterestingPoint p : cs.cut )
 				probe.put(p, probe.size());
 		}
-		for( InterestingPoint p : part.getMatPointsExt() )
+		//sort materialization points in decreasing order of their sizes
+		//which can improve the pruning efficiency by skipping larger sub-spaces.
+		for( InterestingPoint p : sortBySize(part.getMatPointsExt(), memo, false) )
 			if( !probe.containsKey(p) ) {
 				lsearchSpace.add(p);
 				probe.put(p, probe.size());
@@ -258,7 +262,19 @@ private ArrayList<Pair<CutSet,Double>> evaluateCutSets(ArrayList<ArrayList<NodeL
 
 		return cutSets;
 	}
-
+
+	private InterestingPoint[] sortBySize(InterestingPoint[] points, CPlanMemoTable memo, boolean asc) {
+		return Arrays.stream(points)
+			.sorted(Comparator.comparing(p -> (asc ? 1 : -1) *
+				getSize(memo.getHopRefs().get(p.getToHopID()))))
+			.toArray(InterestingPoint[]::new);
+	}
+
+	private static long getSize(Hop hop) {
+		return Math.max(hop.getDim1(),1) 
+			* Math.max(hop.getDim2(),1);
+	}
+
 	public static class SubProblem {
 		public int offset;
 		public int[] freePos;