Merge pull request #112137 from MikeSpreitzer/add-concurrency-allocation-algorithm
Add solver for APF concurrency rebalancing Kubernetes-commit: 5a1fb17e2e07d9ddd89d83371595c72dee42e87d
This commit is contained in:
Kubernetes Publisher
commit
20c697acfa
4
go.mod
4
go.mod
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@ -43,7 +43,7 @@ require (
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gopkg.in/natefinch/lumberjack.v2 v2.0.0
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gopkg.in/square/go-jose.v2 v2.2.2
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k8s.io/api v0.0.0-20221108053748-98c1aa6b3d0a
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k8s.io/apimachinery v0.0.0-20221108052757-4fe4321a9d5e
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k8s.io/apimachinery v0.0.0-20221108055230-fd8a60496be5
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k8s.io/client-go v0.0.0-20221108054913-4b1a9fdfb58c
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k8s.io/component-base v0.0.0-20221108061007-abdc0eb56a1d
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k8s.io/klog/v2 v2.80.1
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@ -123,7 +123,7 @@ require (
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replace (
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k8s.io/api => k8s.io/api v0.0.0-20221108053748-98c1aa6b3d0a
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k8s.io/apimachinery => k8s.io/apimachinery v0.0.0-20221108052757-4fe4321a9d5e
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k8s.io/apimachinery => k8s.io/apimachinery v0.0.0-20221108055230-fd8a60496be5
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k8s.io/client-go => k8s.io/client-go v0.0.0-20221108054913-4b1a9fdfb58c
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k8s.io/component-base => k8s.io/component-base v0.0.0-20221108061007-abdc0eb56a1d
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k8s.io/kms => k8s.io/kms v0.0.0-20221028080743-a9ba1c11c0c6
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4
go.sum
4
go.sum
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@ -987,8 +987,8 @@ honnef.co/go/tools v0.0.1-2020.1.3/go.mod h1:X/FiERA/W4tHapMX5mGpAtMSVEeEUOyHaw9
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honnef.co/go/tools v0.0.1-2020.1.4/go.mod h1:X/FiERA/W4tHapMX5mGpAtMSVEeEUOyHaw9vFzvIQ3k=
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k8s.io/api v0.0.0-20221108053748-98c1aa6b3d0a h1:GaCla9HtNyi63kysI/cyeA4bv6wRkIyuiUeXpaTF+dw=
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k8s.io/api v0.0.0-20221108053748-98c1aa6b3d0a/go.mod h1:PSXY9/fSNyKgKHUU+O9scnZiW8m+V1znqk49oI6hAEY=
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k8s.io/apimachinery v0.0.0-20221108052757-4fe4321a9d5e h1:zX/AC2CNrYwngyVHVHcsCL36uUtC/3tiZOE6/gfojvc=
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k8s.io/apimachinery v0.0.0-20221108052757-4fe4321a9d5e/go.mod h1:VXMmlsE7YRJ5vyAyWpkKIfFkEbDNpVs0ObpkuQf1WfM=
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k8s.io/apimachinery v0.0.0-20221108055230-fd8a60496be5 h1:iFAMJ1evvrO6X7dS7EKujS6An+bp3u/dD6opu8rn0QA=
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k8s.io/apimachinery v0.0.0-20221108055230-fd8a60496be5/go.mod h1:VXMmlsE7YRJ5vyAyWpkKIfFkEbDNpVs0ObpkuQf1WfM=
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k8s.io/client-go v0.0.0-20221108054913-4b1a9fdfb58c h1:73hBKeNTruSueGRemXkcxxOJ2OV58wJvfdo0+ZMkucA=
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k8s.io/client-go v0.0.0-20221108054913-4b1a9fdfb58c/go.mod h1:Hnc/VjMc6mMK4isnk+uuot3Ymjl7evdMdssMoHIDeSc=
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k8s.io/component-base v0.0.0-20221108061007-abdc0eb56a1d h1:IF51IULm49B+VT4PJOBd4z/SxtU0WVfInKrnykCG/t0=
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@ -0,0 +1,256 @@
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/*
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Copyright 2022 The Kubernetes Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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*/
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package flowcontrol
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import (
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"errors"
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"fmt"
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"math"
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"sort"
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)
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// allocProblemItem is one of the classes to which computeConcurrencyAllocation should make an allocation
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type allocProblemItem struct {
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target float64
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lowerBound float64
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upperBound float64
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}
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// relativeAllocItem is like allocProblemItem but with target avoiding zero and the bounds divided by the target
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type relativeAllocItem struct {
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target float64
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relativeLowerBound float64
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relativeUpperBound float64
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}
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// relativeAllocProblem collects together all the classes and holds the result of sorting by increasing bounds.
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// For J <= K, ascendingIndices[J] identifies a bound that is <= the one of ascendingIndices[K].
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// When ascendingIndices[J] = 2*N + 0, this identifies the lower bound of items[N].
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// When ascendingIndices[J] = 2*N + 1, this identifies the upper bound of items[N].
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type relativeAllocProblem struct {
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items []relativeAllocItem
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ascendingIndices []int
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}
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// initIndices fills in ascendingIndices and sorts them
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func (rap *relativeAllocProblem) initIndices() *relativeAllocProblem {
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rap.ascendingIndices = make([]int, len(rap.items)*2)
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for idx := 0; idx < len(rap.ascendingIndices); idx++ {
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rap.ascendingIndices[idx] = idx
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}
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sort.Sort(rap)
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return rap
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}
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func (rap *relativeAllocProblem) getItemIndex(idx int) (int, bool) {
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packedIndex := rap.ascendingIndices[idx]
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itemIndex := packedIndex / 2
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return itemIndex, packedIndex == itemIndex*2
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}
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// decode(J) returns the bound associated with ascendingIndices[J], the associated items index,
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// and a bool indicating whether the bound is the item's lower bound.
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func (rap *relativeAllocProblem) decode(idx int) (float64, int, bool) {
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itemIdx, lower := rap.getItemIndex(idx)
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if lower {
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return rap.items[itemIdx].relativeLowerBound, itemIdx, lower
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}
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return rap.items[itemIdx].relativeUpperBound, itemIdx, lower
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}
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func (rap *relativeAllocProblem) getProportion(idx int) float64 {
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prop, _, _ := rap.decode(idx)
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return prop
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}
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func (rap *relativeAllocProblem) Len() int { return len(rap.items) * 2 }
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func (rap *relativeAllocProblem) Less(i, j int) bool {
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return rap.getProportion(i) < rap.getProportion(j)
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}
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func (rap *relativeAllocProblem) Swap(i, j int) {
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rap.ascendingIndices[i], rap.ascendingIndices[j] = rap.ascendingIndices[j], rap.ascendingIndices[i]
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}
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// minMax records the minimum and maximum value seen while scanning a set of numbers
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type minMax struct {
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min float64
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max float64
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}
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// note scans one more number
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func (mm *minMax) note(x float64) {
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mm.min = math.Min(mm.min, x)
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mm.max = math.Max(mm.max, x)
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}
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const MinTarget = 0.001
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const epsilon = 0.0000001
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// computeConcurrencyAllocation returns the unique `allocs []float64`, and
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// an associated `fairProp float64`, that jointly have
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// all of the following properties (to the degree that floating point calculations allow)
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// if possible otherwise returns an error saying why it is impossible.
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// `allocs` sums to `requiredSum`.
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// For each J in [0, len(classes)):
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// (1) `classes[J].lowerBound <= allocs[J] <= classes[J].upperBound` and
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// (2) exactly one of the following is true:
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// (2a) `allocs[J] == fairProp * classes[J].target`,
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// (2b) `allocs[J] == classes[J].lowerBound && classes[J].lowerBound > fairProp * classes[J].target`, or
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// (2c) `allocs[J] == classes[J].upperBound && classes[J].upperBound < fairProp * classes[J].target`.
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// Each allocProblemItem is required to have `target >= lowerBound >= 0` and `upperBound >= lowerBound`.
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// A target smaller than MinTarget is treated as if it were MinTarget.
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func computeConcurrencyAllocation(requiredSum int, classes []allocProblemItem) ([]float64, float64, error) {
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if requiredSum < 0 {
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return nil, 0, errors.New("negative sums are not supported")
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}
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requiredSumF := float64(requiredSum)
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var lowSum, highSum, targetSum float64
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ubRange := minMax{min: float64(math.MaxFloat32)}
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lbRange := minMax{min: float64(math.MaxFloat32)}
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relativeItems := make([]relativeAllocItem, len(classes))
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for idx, item := range classes {
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target := item.target
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if item.lowerBound < 0 {
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return nil, 0, fmt.Errorf("lower bound %d is %v but negative lower bounds are not allowed", idx, item.lowerBound)
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}
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if target < item.lowerBound {
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return nil, 0, fmt.Errorf("target %d is %v, which is below its lower bound of %v", idx, target, item.lowerBound)
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}
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if item.upperBound < item.lowerBound {
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return nil, 0, fmt.Errorf("upper bound %d is %v but should not be less than the lower bound %v", idx, item.upperBound, item.lowerBound)
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}
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if target < MinTarget {
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// tweak this to a non-zero value so avoid dividing by zero
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target = MinTarget
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}
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lowSum += item.lowerBound
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highSum += item.upperBound
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targetSum += target
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relativeItem := relativeAllocItem{
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target: target,
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relativeLowerBound: item.lowerBound / target,
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relativeUpperBound: item.upperBound / target,
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}
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ubRange.note(relativeItem.relativeUpperBound)
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lbRange.note(relativeItem.relativeLowerBound)
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relativeItems[idx] = relativeItem
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}
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if lbRange.max > 1 {
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return nil, 0, fmt.Errorf("lbRange.max-1=%v, which is impossible because lbRange.max can not be greater than 1", lbRange.max-1)
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}
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if lowSum-requiredSumF > epsilon {
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return nil, 0, fmt.Errorf("lower bounds sum to %v, which is higher than the required sum of %v", lowSum, requiredSum)
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}
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if requiredSumF-highSum > epsilon {
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return nil, 0, fmt.Errorf("upper bounds sum to %v, which is lower than the required sum of %v", highSum, requiredSum)
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}
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ans := make([]float64, len(classes))
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if requiredSum == 0 {
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return ans, 0, nil
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}
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if lowSum-requiredSumF > -epsilon { // no wiggle room, constrained from below
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for idx, item := range classes {
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ans[idx] = item.lowerBound
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}
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return ans, lbRange.min, nil
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}
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if requiredSumF-highSum > -epsilon { // no wiggle room, constrained from above
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for idx, item := range classes {
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ans[idx] = item.upperBound
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}
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return ans, ubRange.max, nil
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}
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// Now we know the solution is a unique fairProp in [lbRange.min, ubRange.max].
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// See if the solution does not run into any bounds.
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fairProp := requiredSumF / targetSum
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if lbRange.max <= fairProp && fairProp <= ubRange.min { // no bounds matter
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for idx := range classes {
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ans[idx] = relativeItems[idx].target * fairProp
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}
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return ans, fairProp, nil
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}
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// Sadly, some bounds matter.
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// We find the solution by sorting the bounds and considering progressively
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// higher values of fairProp, starting from lbRange.min.
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rap := (&relativeAllocProblem{items: relativeItems}).initIndices()
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sumSoFar := lowSum
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fairProp = lbRange.min
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var sensitiveTargetSum, deltaSensitiveTargetSum float64
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var numSensitiveClasses, deltaSensitiveClasses int
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var nextIdx int
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// `nextIdx` is the next `rap` index to consider.
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// `sumSoFar` is what the allocs would sum to if the current
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// value of `fairProp` solves the problem.
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// If the current value of fairProp were the answer then
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// `sumSoFar == requiredSum`.
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// Otherwise the next increment in fairProp involves changing the allocations
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// of `numSensitiveClasses` classes whose targets sum to `sensitiveTargetSum`;
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// for the other classes, an upper or lower bound has applied and will continue to apply.
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// The last increment of nextIdx calls for adding `deltaSensitiveClasses`
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// to `numSensitiveClasses` and adding `deltaSensitiveTargetSum` to `sensitiveTargetSum`.
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for sumSoFar < requiredSumF {
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// There might be more than one bound that is equal to the current value
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// of fairProp; find all of them because they will all be relevant to
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// the next change in fairProp.
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// Set nextBound to the next bound that is NOT equal to fairProp,
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// and advance nextIdx to the index of that bound.
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var nextBound float64
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for {
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sensitiveTargetSum += deltaSensitiveTargetSum
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numSensitiveClasses += deltaSensitiveClasses
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if nextIdx >= rap.Len() {
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return nil, 0, fmt.Errorf("impossible: ran out of bounds to consider in bound-constrained problem")
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}
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var itemIdx int
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var lower bool
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nextBound, itemIdx, lower = rap.decode(nextIdx)
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if lower {
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deltaSensitiveClasses = 1
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deltaSensitiveTargetSum = rap.items[itemIdx].target
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} else {
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deltaSensitiveClasses = -1
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deltaSensitiveTargetSum = -rap.items[itemIdx].target
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}
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nextIdx++
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if nextBound > fairProp {
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break
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}
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}
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// fairProp can increase to nextBound without passing any intermediate bounds.
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if numSensitiveClasses == 0 {
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// No classes are affected by the next range of fairProp; skip right past it
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fairProp = nextBound
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continue
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}
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// See whether fairProp can increase to the solution before passing the next bound.
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deltaFairProp := (requiredSumF - sumSoFar) / sensitiveTargetSum
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nextProp := fairProp + deltaFairProp
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if nextProp <= nextBound {
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fairProp = nextProp
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break
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}
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// No, fairProp has to increase above nextBound
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sumSoFar += (nextBound - fairProp) * sensitiveTargetSum
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fairProp = nextBound
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}
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for idx, item := range classes {
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ans[idx] = math.Max(item.lowerBound, math.Min(item.upperBound, fairProp*relativeItems[idx].target))
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}
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return ans, fairProp, nil
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}
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|
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@ -0,0 +1,156 @@
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/*
|
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Copyright 2022 The Kubernetes Authors.
|
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|
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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 flowcontrol
|
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|
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import (
|
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"math"
|
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"math/rand"
|
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"sort"
|
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"testing"
|
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)
|
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|
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// floating-point imprecision
|
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const fpSlack = 1e-10
|
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|
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// TestConcAlloc tests computeConcurrencyAllocation with a bunch of randomly generated cases.
|
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func TestConcAlloc(t *testing.T) {
|
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rands := rand.New(rand.NewSource(1234567890))
|
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for i := 0; i < 10000; i++ {
|
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test1ConcAlloc(t, rands)
|
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}
|
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}
|
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|
||||
func test1ConcAlloc(t *testing.T, rands *rand.Rand) {
|
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probLen := ([]int{0, 1, 2, 3, 4, 6, 9})[rands.Intn(7)]
|
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classes := make([]allocProblemItem, probLen)
|
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var lowSum, highSum float64
|
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var requiredSum int
|
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var requiredSumF float64
|
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style := "empty"
|
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if probLen > 0 {
|
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switch rands.Intn(20) {
|
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case 0:
|
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style = "bound from below"
|
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requiredSum = rands.Intn(probLen * 3)
|
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requiredSumF = float64(requiredSum)
|
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partition64(rands, probLen, requiredSumF, func(j int, x float64) {
|
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classes[j].lowerBound = x
|
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classes[j].target = x + 2*rands.Float64()
|
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classes[j].upperBound = x + 3*rands.Float64()
|
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lowSum += classes[j].lowerBound
|
||||
highSum += classes[j].upperBound
|
||||
})
|
||||
case 1:
|
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style = "bound from above"
|
||||
requiredSum = rands.Intn(probLen*3) + 1
|
||||
requiredSumF = float64(requiredSum)
|
||||
partition64(rands, probLen, requiredSumF, func(j int, x float64) {
|
||||
classes[j].upperBound = x
|
||||
classes[j].lowerBound = x * math.Max(0, 1.25*rands.Float64()-1)
|
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classes[j].target = classes[j].lowerBound + rands.Float64()
|
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lowSum += classes[j].lowerBound
|
||||
highSum += classes[j].upperBound
|
||||
})
|
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default:
|
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style = "not-set-by-bounds"
|
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for j := 0; j < probLen; j++ {
|
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x := math.Max(0, rands.Float64()*5-1)
|
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classes[j].lowerBound = x
|
||||
classes[j].target = x + 2*rands.Float64()
|
||||
classes[j].upperBound = x + 3*rands.Float64()
|
||||
lowSum += classes[j].lowerBound
|
||||
highSum += classes[j].upperBound
|
||||
}
|
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requiredSumF = math.Round(float64(lowSum + (highSum-lowSum)*rands.Float64()))
|
||||
requiredSum = int(requiredSumF)
|
||||
}
|
||||
}
|
||||
for rands.Float64() < 0.25 {
|
||||
// Add a class with a target of zero
|
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classes = append(classes, allocProblemItem{target: 0, upperBound: rands.Float64() + 0.00001})
|
||||
highSum += classes[probLen].upperBound
|
||||
if probLen > 1 {
|
||||
m := rands.Intn(probLen)
|
||||
classes[m], classes[probLen] = classes[probLen], classes[m]
|
||||
}
|
||||
probLen = len(classes)
|
||||
}
|
||||
allocs, fairProp, err := computeConcurrencyAllocation(requiredSum, classes)
|
||||
var actualSumF float64
|
||||
for _, item := range allocs {
|
||||
actualSumF += item
|
||||
}
|
||||
expectErr := lowSum-requiredSumF > fpSlack || requiredSumF-highSum > fpSlack
|
||||
if err != nil {
|
||||
if expectErr {
|
||||
t.Logf("For requiredSum=%v, %s classes=%#+v expected error and got %#+v", requiredSum, style, classes, err)
|
||||
return
|
||||
}
|
||||
t.Fatalf("For requiredSum=%v, %s classes=%#+v got unexpected error %#+v", requiredSum, style, classes, err)
|
||||
}
|
||||
if expectErr {
|
||||
t.Fatalf("Expected error from requiredSum=%v, %s classes=%#+v but got solution %v, %v instead", requiredSum, style, classes, allocs, fairProp)
|
||||
}
|
||||
rd := f64RelDiff(requiredSumF, actualSumF)
|
||||
if rd > fpSlack {
|
||||
t.Fatalf("For requiredSum=%v, %s classes=%#+v got solution %v, %v which has sum %v", requiredSum, style, classes, allocs, fairProp, actualSumF)
|
||||
}
|
||||
for idx, item := range classes {
|
||||
target := math.Max(item.target, MinTarget)
|
||||
alloc := fairProp * target
|
||||
if alloc <= item.lowerBound {
|
||||
if allocs[idx] != item.lowerBound {
|
||||
t.Fatalf("For requiredSum=%v, %s classes=%#+v got solution %v, %v in which item %d should be its lower bound but is not", requiredSum, style, classes, allocs, fairProp, idx)
|
||||
}
|
||||
} else if alloc >= item.upperBound {
|
||||
if allocs[idx] != item.upperBound {
|
||||
t.Fatalf("For requiredSum=%v, %s classes=%#+v got solution %v, %v in which item %d should be its upper bound but is not", requiredSum, style, classes, allocs, fairProp, idx)
|
||||
}
|
||||
} else if f64RelDiff(alloc, allocs[idx]) > fpSlack {
|
||||
t.Fatalf("For requiredSum=%v, %s classes=%#+v got solution %v, %v in which item %d got alloc %v should be %v (which is proportional to its target) but is not", requiredSum, style, classes, allocs, fairProp, idx, allocs[idx], alloc)
|
||||
}
|
||||
}
|
||||
t.Logf("For requiredSum=%v, %s classes=%#+v got solution %v, %v", requiredSum, style, classes, allocs, fairProp)
|
||||
}
|
||||
|
||||
// partition64 calls consume n times, passing ints [0,n) and floats that sum to x
|
||||
func partition64(rands *rand.Rand, n int, x float64, consume func(int, float64)) {
|
||||
if n <= 0 {
|
||||
return
|
||||
}
|
||||
divs := make([]float64, n-1)
|
||||
for idx := range divs {
|
||||
divs[idx] = float64(rands.Float64())
|
||||
}
|
||||
sort.Float64s(divs)
|
||||
var last float64
|
||||
for idx, div := range divs {
|
||||
div32 := float64(div)
|
||||
delta := div32 - last
|
||||
consume(idx, delta*x)
|
||||
last = div32
|
||||
}
|
||||
consume(n-1, (1-last)*x)
|
||||
}
|
||||
|
||||
func f64RelDiff(a, b float64) float64 {
|
||||
den := math.Max(math.Abs(a), math.Abs(b))
|
||||
if den == 0 {
|
||||
return 0
|
||||
}
|
||||
return math.Abs(a-b) / den
|
||||
}
|
||||
Loading…
Reference in New Issue