karmada/pkg/scheduler/core/spreadconstraint/select_groups.go

/*
Copyright 2023 The Karmada Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

package spreadconstraint

import (
	"fmt"
	"sort"
	"strings"

	"k8s.io/klog/v2"
)

// GroupInfo indicate the group info.
type GroupInfo struct {
	name   string
	value  int
	weight int64
}

type dfsPath struct {
	id     int
	groups []*GroupInfo
	weight int64
	value  int
}

func (path *dfsPath) next() *dfsPath {
	path.id++
	result := new(dfsPath)
	*result = *path
	if path.groups != nil {
		result.groups = make([]*GroupInfo, len(path.groups))
		copy(result.groups, path.groups)
	}
	for _, group := range result.groups {
		result.weight += group.weight
		result.value += group.value
	}
	result.sortGroups()
	return result
}

func (path *dfsPath) enqueue(group *GroupInfo) {
	path.groups = append(path.groups, group)
}

func (path *dfsPath) popLast() {
	path.groups = path.groups[:path.length()-1]
}

func (path *dfsPath) length() int {
	return len(path.groups)
}

func (path *dfsPath) sortGroups() {
	sort.Slice(path.groups, func(i, j int) bool {
		if path.groups[i].weight != path.groups[j].weight {
			return path.groups[i].weight > path.groups[j].weight
		}

		return path.groups[i].name < path.groups[j].name
	})
}

func (path *dfsPath) matchSubPath(subPath *dfsPath) bool {
	if subPath.length() >= path.length() {
		return false
	}

	for i, group := range subPath.groups {
		if path.groups[i].name != group.name {
			return false
		}
	}

	return true
}

func (path *dfsPath) String() string {
	var groupNames []string
	for _, group := range path.groups {
		groupNames = append(groupNames, group.name)
	}
	return fmt.Sprintf("[%s]", strings.Join(groupNames, "->"))
}

// selectGroups select best groups in all groups.
func selectGroups(groups []*GroupInfo, minConstraint, maxConstraint, target int) []*GroupInfo {
	if len(groups) == 0 {
		return nil
	}

	feasiblePaths := findFeasiblePaths(groups, minConstraint, maxConstraint, target)
	if len(feasiblePaths) == 0 {
		return nil
	}
	klog.V(4).Infof("find feasible paths: %v", feasiblePaths)

	return prioritizePaths(feasiblePaths).groups
}

// findFeasiblePaths find all feasible path based on DFS.
// We give an example of a tree diagram for easy understanding, assuming: target=7, groups: [2,3,6,7].
// Note: groups is only briefly represented by the value.
//
//	                        +---------------------------------+
//	                        |            target=7             |
//	                        +---------------+-------------+---+
//	                       /                |             |    \
//	                     2/                3|            6|     \7
//	                     /                  |             |      \
//	                +---+                 +-+-+         +-+-+     +---+
//	                | 5 |                 | 4 |         | 1 |     | 0 |
//	                +-+-+                 +---+         +-+-+     +---+
//	               /  |  \               /     \          |
//	             3/  6|   \7           6/       \7       7|
//	             /    |    \           /         \        |
//	        +---+   +-+-+   +---+ +---+           +---+ +-+-+
//	        | 2 |   |-1 |   |-2 | |-2 |           |-3 | |-6 |
//	        +---+   +---+   +---+ +---+           +---+ +---+
//	       /     \
//	     6/       \7
//	     /         \
//	+---+           +---+
//	|-4 |           |-5 |
//	+---+           +---+
//
// The path from the root path to all leaf nodes whose value is less than or equal to 0 is a feasible combination.
// minConstraint and maxConstraint are used to limit the length of the path. Therefore, we can exclude some
// combinations whose path is too long or too short during the search process.
// If we set minConstraint=2 and maxConstraint=2, so the feasible paths is: [2,6] [2,7] [3,6] [3,7] [6,7]
func findFeasiblePaths(groups []*GroupInfo, minConstraint, maxConstraint, target int) (paths []*dfsPath) {
	if len(groups) > 1 {
		sort.Slice(groups, func(i, j int) bool {
			if groups[i].value != groups[j].value {
				return groups[i].value < groups[j].value
			}

			if groups[i].weight != groups[j].weight {
				return groups[i].weight > groups[j].weight
			}

			return groups[i].name < groups[j].name
		})
	}

	rootPath := new(dfsPath)
	var dfsFunc func(int, int)
	dfsFunc = func(sum, begin int) {
		if sum >= target && rootPath.length() >= minConstraint && rootPath.length() <= maxConstraint {
			paths = append(paths, rootPath.next())
			return
		}

		// pruning makes DFS faster
		if rootPath.length() >= maxConstraint {
			return
		}

		for i := begin; i < len(groups); i++ {
			sum += groups[i].value
			rootPath.enqueue(groups[i])
			dfsFunc(sum, i+1)

			// stop backtracking when we have to traverse all groups to satisfy the minimum constraint.
			if len(groups) == minConstraint {
				break
			}

			sum -= groups[i].value
			rootPath.popLast()
		}
	}
	dfsFunc(0, 0)
	return
}

// prioritizePaths select a best path from feasible paths based on a multi-dimensional prioritization strategy.
// That's: weight > value > id(just for predictable result).
// But for the existence of subpaths, we should give priority to subpaths.
// For example:
// G1 -> G2 -> G3
// G1 -> G2
// G1 -> G3
// The best path is [G1 -> G2 -> G3], but [G1 -> G2] is its subpath. So we should choose [G1 -> G2].
func prioritizePaths(feasiblePaths []*dfsPath) *dfsPath {
	if len(feasiblePaths) == 1 {
		return feasiblePaths[0]
	}

	sort.Slice(feasiblePaths, func(i, j int) bool {
		if feasiblePaths[i].weight != feasiblePaths[j].weight {
			return feasiblePaths[i].weight > feasiblePaths[j].weight
		}

		if feasiblePaths[i].value != feasiblePaths[j].value {
			return feasiblePaths[i].value > feasiblePaths[j].value
		}

		return feasiblePaths[i].id < feasiblePaths[j].id
	})

	finalPath := feasiblePaths[0]
	for i := 1; i < len(feasiblePaths); i++ {
		if finalPath.matchSubPath(feasiblePaths[i]) {
			finalPath = feasiblePaths[i]
		}
	}
	return finalPath
}