Overview
Weighted Interval Scheduling is a scheduling method that selects or admits work using a concrete priority, fairness, deadline, or capacity rule. It helps expose the policy tradeoff behind queue order, fairness, deadlines, or resource use.
CoreSource checked
Weighted Interval Scheduling
Weighted Interval Scheduling selects compatible intervals from overlapping candidates.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Scheduling
- Difficulty
- Intermediate
- Family
- Scheduling
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 2
- Code example
- Ready
- Visualization
- Ready
Core Concepts
priority ruleresource allocationqueue disciplinetask order
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n log n)
Worst
O(n^2)
Space
O(n)
When to Use
- Use Weighted Interval Scheduling when queue order, resource assignment, or deadline policy must be explicit.
- Use it when comparing fairness, latency, throughput, or utilization policies matters.
When Not to Use
- Avoid when the policy would hide starvation, unfairness, or deadline misses.
- Avoid when task durations or priorities are too uncertain for the rule to be meaningful.
What It Does
- Ranks ready work with a scheduling rule
- Updates waiting time, deadlines, or capacity
- Returns an order, assignment, or admission decision
Use Cases
- CPU scheduling
- Network queue management
- Workflow and batch processing
Inputs
- Jobs or requests
- Timing constraints
- Resource limits
Outputs
- Execution order
- Resource assignment
- Timing decision
Key Formulas (1)
Weighted interval recurrence
OPT(i) = max(valuei + OPT(p(i)), OPT(i − 1))
OPT(i) = max(value_i + OPT(p(i)), OPT(i - 1))Chooses between taking interval i and skipping it.
Pseudocode
- 1.Collect ready jobs, queues, or tasks
- 2.Compute the method's priority, fairness, or capacity score
- 3.Select the next job or resource assignment
- 4.Update waiting time, capacity, or completion state
- 5.Repeat until all work is scheduled or admitted
Canonical Example
- Input
- jobs = [{id:A, time:3}, {id:B, time:1}], resource = one worker
- Output
- ordered or assigned jobs according to the scheduling rule
- Explanation
- Weighted Interval Scheduling computes the priority or capacity rule and chooses the next job from the ready set.
Implementation Notes
- Make tie-breaking deterministic and visible in tests.
- Track waiting time, service time, and resource state separately.
Common Pitfalls
- Forgetting tie-breaking rules makes schedules unstable across runs.
- Ignoring starvation and fairness edge cases can make good averages hide bad tail behavior.
Interactive Mechanism Walkthrough
Graph Frontier & Edge RelaxationShow queued jobs moving onto processors, links, or time slots as the scheduling rule changes priorities.
Step 1 of 5: Collect ready jobs, queues, or tasks
schedulingNotes
Weighted Interval Scheduling operates in O(n log n) time and O(n) space within the Scheduling family. Key governing relation: OPT(i) = max(value_i + OPT(p(i)), OPT(i - 1)). Often compared with Round Robin Scheduling and Priority Scheduling.
Sources (1)
What each reference supports for this entry.
Scheduling: Theory, Algorithms, and Systems
BookScheduling reference for Weighted Interval Scheduling dynamic programming over compatible jobs and weighted interval choices.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborRound Robin Scheduling
Weighted Interval Scheduling and Round Robin Scheduling address nearby scheduling problems but make different implementation tradeoffs.
Related Algorithms
Tags
Scheduling