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* Algorithm for project planning. More precisely, *list scheduling* with support for machines running at different
* speeds, optional preemption, optional splitting of jobs across machines, release dates, and delivery times.
*
* See README file for details.
*/
/** API documentation barrier */
import { strict as assert } from 'assert';
import {
Job,
JobFragment,
JobSplitting,
Schedule,
ScheduledJob,
SchedulingFailure,
SchedulingInstance,
} from './api-types';
import MinHeap from './minheap';
/**
* Type that consists of the union of all properties that are marked as optional through a question mark.
*
* Note that properties that have undefined in their domain, but no question mark next to the property name are *not*
* included. Also note that, in strict compilation mode, TypeScript will add undefined to the domain of the property if
* there is a question mark next to the property name.
*
* @typeparam T generic type parameter
*/
type OptionalPropertyNames<T extends {}> = {[K in keyof T]-?: {} extends {[_ in K]: T[K]} ? K : never}[keyof T];
type Defined<T> = T extends undefined ? never : T;
type OnlyOptionals<T extends {}> = {[K in OptionalPropertyNames<T>]: Defined<T[K]>};
const JOB_DEFAULTS = Object.freeze<OnlyOptionals<Job>>({
deliveryTime: 0,
splitting: JobSplitting.PREEMPTION,
dependencies: [],
releaseTime: 0,
preAssignment: -1,
});
/**
* Runs the list scheduling algorithm on the given problem instance and returns the result.
*
* See [the project page](https://github.com/fschopp/project-planning-js) for more information on the algorithm.
*
* @param instance the problem instance
* @return solution or a human-readable failure description if the problem instance is invalid (for example, has a
* cyclic dependency graph)
*/
export function computeSchedule(instance: SchedulingInstance): Schedule | SchedulingFailure {
const nonNegativeInteger = (number: number) => number >= 0 && Number.isInteger(number);
const positiveIntegers = (numbers: number[]) =>
numbers.filter((number) => number <= 0 || !Number.isInteger(number)).length === 0;
const undefinedOrNonNegativeInteger = (number: number | undefined) =>
number === undefined || nonNegativeInteger(number);
const undefinedOrNonNegativeIntegers = (...numbers: (number | undefined)[]) =>
numbers.filter((number) => !undefinedOrNonNegativeInteger(number)).length === 0;
const undefinedOrIntegerWithinZeroTo = (upperBoundExcl: number, number: number | undefined) =>
number === undefined || nonNegativeInteger(number) && number < upperBoundExcl;
const integersWithinZeroTo = (upperBoundExcl: number, numbers: number[]) =>
numbers.filter((number) => !(number >= 0 && nonNegativeInteger(number) && number < upperBoundExcl)).length === 0;
const numMachines: number = instance.machineSpeeds.length;
const numJobs: number = instance.jobs.length;
if (numMachines === 0) {
return 'At least one machine is required to compute a schedule.';
} else if (
!positiveIntegers(instance.machineSpeeds) ||
instance.jobs.filter((job) =>
!nonNegativeInteger(job.size) ||
!undefinedOrNonNegativeIntegers(job.deliveryTime, job.releaseTime) ||
!undefinedOrIntegerWithinZeroTo(numMachines, job.preAssignment) ||
(job.dependencies !== undefined && !integersWithinZeroTo(numJobs, job.dependencies))
).length > 0 ||
!undefinedOrNonNegativeInteger(instance.minFragmentSize)
) {
return 'All job processing times and machine speeds need to be non-negative integers. ' +
'All job dependency and pre-assignment indices need to be within bounds.';
}
const jobs: Required<Job>[] = instance.jobs.map((job) => Object.assign({}, JOB_DEFAULTS, job));
const minFragmentSize: number = instance.minFragmentSize === undefined ? 0 : instance.minFragmentSize;
return new ListScheduling(numMachines, instance.machineSpeeds, jobs, minFragmentSize).schedule;
}
/**
* A gap in the schedule for a particular machine. A gap can be filled when scheduling subsequent jobs.
*/
interface Gap {
startTime: number;
endTime: number;
}
/**
* Linked list of gaps.
*/
interface GapsList {
head: Gap;
tail: GapsList | null;
}
/**
* A machine and associated data required by {@link ListScheduling.scheduleJob}().
*/
interface Machine {
/**
* Index in array of all machines.
*
* This is a value between 0 (inclusive) and the length of {@link SchedulingInstance.machineSpeeds} (exclusive).
*/
readonly index: number;
/**
* Index in array of available machines for the current job.
*/
readonly availableIdx: number;
/**
* Speed of the machine.
*/
readonly speed: number;
/**
* Time when the current job fragment started on the machine, or null if the current job is not currently running on
* the machine.
*/
currentFragmentStart: number | null;
/**
* Linked list of gaps.
*
* Whenever starting to schedule a job, this is initialized with a tail list of {@link ListScheduling.gapsLists_}.
*/
gapsList: GapsList;
/**
* Node of the linked list of gaps before the current node (which is {@link gapsList}).
*
* This field is only needed to “commit” the insertion of job fragments by making changes to the gap list shared
* between scheduling of individual jobs.
*/
previousGapsList: GapsList;
}
/**
* Node in the job graph induced by the dependencies.
*/
interface JobGraphNode {
idx: number;
numDependencies: number;
dependents: JobGraphNode[];
}
/**
* Abstraction for a collection of machines available for a job.
*/
interface AvailableMachineIndices {
readonly length: number;
forEach(callbackfn: (index: number, availableIdx: number) => void): void;
map<T>(callbackfn: (index: number, availableIdx: number) => T): T[];
}
/**
* Internal class whose sole purpose is to store algorithm state, so it does not have to be inconveniently passed around
* between functions.
*/
class ListScheduling {
public readonly schedule: Schedule | SchedulingFailure;
private readonly numMachines_: number;
private readonly machineSpeeds_: number[];
private readonly jobs_: Required<Job>[];
private readonly minFragmentSize_: number;
private readonly gapsLists_: GapsList[];
constructor(numMachines: number, machineSpeeds: number[], jobs: Required<Job>[], minFragmentSize: number) {
this.numMachines_ = numMachines;
this.machineSpeeds_ = machineSpeeds;
this.jobs_ = jobs;
this.minFragmentSize_ = minFragmentSize;
this.gapsLists_ = this.machineSpeeds_.map((ignoredMachineSpeed) => ({
head: {
startTime: Number.MIN_SAFE_INTEGER,
endTime: 0,
},
tail: {
head: {
startTime: 0,
endTime: Number.MAX_SAFE_INTEGER,
},
tail: null,
},
}));
this.schedule = this.computeSchedule();
}
/**
* Returns the next “event” for the given machine.
*
* This method has side-effects. It updates field {@link Machine.previousGapsList} and {@link Machine.gapsList} of the
* given machine.
*/
private static nextTimeStamp(minWallClockTime: number, earliestStart: number, machine: Machine): number {
let currentGap: Gap = machine.gapsList.head;
assert(Number.isInteger(minWallClockTime) && Number.isInteger(earliestStart) &&
Number.isInteger(currentGap.startTime) && Number.isInteger(currentGap.endTime), 'Invalid arguments');
if (machine.currentFragmentStart === null) {
while (true) {
const timeStamp = Math.max(earliestStart, currentGap.startTime) + minWallClockTime;
if (timeStamp <= currentGap.endTime) {
return timeStamp;
}
assert(machine.gapsList.tail !== null, 'Invariant: last gap has endTime === Number.MAX_SAFE_INTEGER');
machine.previousGapsList = machine.gapsList;
machine.gapsList = machine.gapsList.tail!;
currentGap = machine.gapsList.head;
}
} else {
return currentGap.endTime;
}
}
/**
* Adjust the linked list of gaps to account for the newly scheduled job fragment.
*
* There are 4 cases to consider. The new job fragment either:
* 1. Fills out the current gap completely. In this case, the current gap needs to be removed
* entirely.
* 2. Aligns with the start of the current gap, but ends before it. In this case, the start of the current gap is
* changed to when the new job fragment ends.
* 3. Does not start with the current gap, but aligns with the end of it. In this case, the end of the current gap is
* changed to when the job fragment starts.
* 4. If the current gap aligns with neither start nor end of the current gap, a new gap is inserted before the
* current gap. It starts with the current gap and ends with the start of the job fragment. The start of the
* current gap is then changed to the end of the job fragment.
*
* @param machineState State of the machine that the job fragment has been scheduled on.
* @param end end time of the job fragment
* @param commitGaps if true, then commit the updated gaps to the state that is shared across scheduling of individual
* jobs
*/
private adjustGaps(machineState: Machine, end: number, commitGaps: boolean): void {
assert(machineState.index >= 0 && machineState.index < this.numMachines_ &&
machineState.currentFragmentStart !== null && Number.isInteger(machineState.currentFragmentStart) &&
Number.isInteger(end) && machineState.currentFragmentStart <= end, 'Invalid arguments');
// machineState also points to state that is shared across scheduling of individual jobs. This shared state we must
// not modify if dryRun is true. We therefore cannot make modifications to the properties of
// machineState.previousGapsList or machineState.gap.
const start: number = machineState.currentFragmentStart!;
const currentGap = machineState.gapsList.head;
if (commitGaps) {
if (start === currentGap.startTime && end === currentGap.endTime) {
machineState.previousGapsList.tail = machineState.gapsList.tail;
} else if (start === currentGap.startTime) {
currentGap.startTime = end;
} else if (end === currentGap.endTime) {
currentGap.endTime = start;
machineState.previousGapsList = machineState.gapsList;
// Note that machineState.gapsList will be updated below.
} else {
machineState.previousGapsList.tail = {
head: {
startTime: currentGap.startTime,
endTime: start,
},
tail: machineState.gapsList,
};
currentGap.startTime = end;
}
}
if (end === currentGap.endTime) {
// Note that machineState.gapsList.tail === null would imply that the current gap is the last gap; that is,
// currentGap.endTime === Number.MAX_SAFE_INTEGER. But we are also in the case where (end === currentGap.endTime).
// Since we don't support schedules that long, it is safe to assert:
assert(machineState.gapsList.tail !== null, 'Expected currentGap.endTime < Number.MAX_SAFE_INTEGER');
machineState.gapsList = machineState.gapsList.tail!;
} else if (!commitGaps) {
machineState.gapsList = {
head: {
startTime: end,
endTime: currentGap.endTime,
},
tail: machineState.gapsList.tail,
};
}
// Upon return, we will be "before" the gap represented by machineState.gapsList.head.
machineState.currentFragmentStart = null;
}
private createJobFragment(machineState: Machine, end: number, scheduledJob?: ScheduledJob): void {
if (scheduledJob) {
const start: number = machineState.currentFragmentStart!;
if (end - start > 0) {
const jobFragment: JobFragment = {
machine: machineState.index,
start,
end,
isWaiting: false,
};
scheduledJob.push(jobFragment);
}
}
this.adjustGaps(machineState, end, scheduledJob !== undefined);
}
/**
* Schedules processing of a job and returns its completion time (excluding delivery time).
*/
private scheduleJob(availableMachineIndices: AvailableMachineIndices, size: number, isPreemptible: boolean,
earliestStart: number, scheduledJob?: ScheduledJob): number {
assert(availableMachineIndices.length > 0 && Number.isInteger(size) && size >= 0 &&
Number.isInteger(earliestStart), 'Invalid arguments');
const minFragmentSize = isPreemptible ? Math.min(size, this.minFragmentSize_) : size;
let currentSpeed = 0;
let lastTimestamp = earliestStart;
let remainingSize = size;
const machines: Machine[] = availableMachineIndices.map((index, availableIdx): Machine => {
const gapsList = this.gapsLists_[index];
assert(gapsList.tail !== null, 'Invariant: at least 2 elements in linked list gapsList');
return {
index,
availableIdx,
speed: this.machineSpeeds_[index],
currentFragmentStart: null,
previousGapsList: gapsList,
gapsList: gapsList.tail!,
};
});
while (remainingSize > 0) {
let eventTime: number = Number.MAX_SAFE_INTEGER;
let machine: Machine = machines[0];
availableMachineIndices.forEach((index, availableIdx) => {
const minWallClockTime = Math.ceil(minFragmentSize / machines[availableIdx].speed);
const machineEventTime = ListScheduling.nextTimeStamp(minWallClockTime, earliestStart, machines[availableIdx]);
if (machineEventTime < eventTime) {
eventTime = machineEventTime;
machine = machines[availableIdx];
}
});
let isProjectedEndTime: boolean = false;
const currentProjectedEndTime: number = Math.ceil(lastTimestamp + remainingSize / currentSpeed);
if (currentProjectedEndTime < eventTime) {
eventTime = currentProjectedEndTime;
isProjectedEndTime = true;
}
assert(Number.isInteger(eventTime) && Number.isInteger(lastTimestamp) && Number.isInteger(currentSpeed),
'Invariant: timestamps and speeds are integers');
remainingSize -= (eventTime - lastTimestamp) * currentSpeed;
assert(!isProjectedEndTime || remainingSize <= 0,
'Invariant: isProjectedEndTime implies remainingSize <= 0');
if (!isProjectedEndTime) {
if (machine.currentFragmentStart === null) {
const nextGap: Gap = machine.gapsList.head;
machine.currentFragmentStart = Math.max(earliestStart, nextGap.startTime);
remainingSize -= (eventTime - machine.currentFragmentStart) * machine.speed;
currentSpeed += machine.speed;
} else {
this.createJobFragment(machine, eventTime, scheduledJob);
currentSpeed -= machine.speed;
assert(machine.currentFragmentStart === null && currentSpeed >= 0);
}
}
lastTimestamp = eventTime;
assert(Number.isInteger(lastTimestamp) && Number.isInteger(remainingSize),
'Invariant: timestamps and durations are integers');
}
availableMachineIndices.forEach((ignoredIndex, availableIdx) => {
if (machines[availableIdx].currentFragmentStart !== null) {
this.createJobFragment(machines[availableIdx], lastTimestamp, scheduledJob);
}
});
return lastTimestamp;
}
/**
* Adds the given delivery time on the given machine to the given job schedule, and returns the overall completion
* time of the job.
*/
private static scheduleDeliveryTime(machineIdx: number, processingCompletionTime: number, deliveryTime: number,
scheduledJob: ScheduledJob): number {
assert(Number.isInteger(deliveryTime), 'Invalid arguments');
assert(scheduledJob.length > 0 ? processingCompletionTime === scheduledJob[scheduledJob.length - 1].end : true,
'Processing completion time is end timestamp of last job fragment');
let completionTime: number = processingCompletionTime;
if (deliveryTime > 0) {
completionTime += deliveryTime;
const deliveryJobFragment: JobFragment = {
machine: machineIdx,
start: processingCompletionTime,
end: completionTime,
isWaiting: true,
};
scheduledJob.push(deliveryJobFragment);
}
return completionTime;
}
private allMachines(): AvailableMachineIndices {
return {
length: this.machineSpeeds_.length,
forEach(callbackfn: (index: number, availableIdx: number) => void): void {
for (let i = 0; i < this.length; ++i) {
callbackfn(i, i);
}
},
map<T>(callbackfn: (index: number, availableIdx: number) => T): T[] {
const array: T[] = [];
array.length = this.length;
for (let i = 0; i < this.length; ++i) {
array[i] = callbackfn(i, i);
}
return array;
},
};
}
private static singleMachine(singleMachineIdx: number): AvailableMachineIndices {
return {
length: 1,
forEach(callbackfn: (index: number, availableIdx: number) => void): void {
callbackfn(singleMachineIdx, 0);
},
map<T>(callbackfn: (index: number, availableIdx: number) => T): T[] {
return [callbackfn(singleMachineIdx, 0)];
},
};
}
private computeSchedule(): Schedule | SchedulingFailure {
const noDependencyNodes: JobGraphNode[] = [];
const jobGraphNodes: JobGraphNode[] = this.jobs_.map((job, index): JobGraphNode => ({
idx: index,
numDependencies: job.dependencies.length,
dependents: [],
}));
for (let i = 0; i < this.jobs_.length; ++i) {
const job = this.jobs_[i];
const jobGraphNode = jobGraphNodes[i];
for (const dependencyIdx of job.dependencies) {
jobGraphNodes[dependencyIdx].dependents.push(jobGraphNode);
}
if (job.dependencies.length === 0) {
noDependencyNodes.push(jobGraphNode);
}
}
const allMachines: AvailableMachineIndices = this.allMachines();
const newSchedule: Schedule = this.jobs_.map((ignoredJob) => []);
const finishTimes: number[] = this.jobs_.map((ignoredJob) => -1);
let numScheduledJobs = 0;
const noDependencyNodesHeap = new MinHeap<JobGraphNode>(noDependencyNodes, (left, right) => left.idx - right.idx);
while (!noDependencyNodesHeap.isEmpty()) {
const jobGraphNode: JobGraphNode = noDependencyNodesHeap.extractMin()!;
const job = this.jobs_[jobGraphNode.idx];
const isPreemptible: boolean = job.splitting !== JobSplitting.NONE;
const earliestStartTime = job.dependencies.reduce((previousEarliestStartTime, dependencyIdx) => {
const dependencyFinishTime: number = finishTimes[dependencyIdx];
assert(dependencyFinishTime >= 0, 'Dependencies are scheduled before their dependents');
return Math.max(previousEarliestStartTime, dependencyFinishTime);
}, job.releaseTime);
let availableMachines: AvailableMachineIndices = allMachines;
let deliveryMachineIdx: number | undefined;
if (job.splitting === JobSplitting.MULTIPLE_MACHINES) {
deliveryMachineIdx = job.preAssignment >= 0
? job.preAssignment
: 0;
} else if (job.preAssignment >= 0) {
availableMachines = ListScheduling.singleMachine(job.preAssignment);
deliveryMachineIdx = job.preAssignment;
} else {
let maxCompletionTime: number = Number.MAX_SAFE_INTEGER;
for (let i = 0; i < this.numMachines_; ++i) {
const currentAvailableMachines = ListScheduling.singleMachine(i);
const currentCompletionTime =
this.scheduleJob(currentAvailableMachines, job.size, isPreemptible, earliestStartTime);
if (currentCompletionTime < maxCompletionTime) {
availableMachines = currentAvailableMachines;
deliveryMachineIdx = i;
maxCompletionTime = currentCompletionTime;
}
}
}
assert(deliveryMachineIdx !== undefined);
const completionTime: number = this.scheduleJob(
availableMachines, job.size, isPreemptible, earliestStartTime, newSchedule[jobGraphNode.idx]);
finishTimes[jobGraphNode.idx] = ListScheduling.scheduleDeliveryTime(
deliveryMachineIdx!, completionTime, job.deliveryTime, newSchedule[jobGraphNode.idx]);
++numScheduledJobs;
for (const dependent of jobGraphNode.dependents) {
--dependent.numDependencies;
if (dependent.numDependencies === 0) {
noDependencyNodesHeap.add(dependent);
}
}
}
return numScheduledJobs !== this.jobs_.length
? 'Detected a cycle in the dependency graph.'
: newSchedule;
}
}
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