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To run dependent browser tasks in order while allowing independent tasks to overlap, use Kahn’s algorithm to track which nodes are ready, then add a separate asynchronous scheduler to dispatch them. A topological sort gives you a valid order; it does not execute work, collect results, enforce a concurrency limit, or define what happens when a task fails or is cancelled.
What Kahn’s algorithm does—and what the runtime must add
Represent each task as a node and each prerequisite as a directed edge. In this article, A -> B means A must finish successfully before B may start. A topological ordering places A before B. If multiple tasks have no outstanding prerequisites, more than one valid ordering may exist.
Kahn’s algorithm maintains each node’s incoming-edge count, or indegree. Initially, nodes with indegree zero are ready. Processing a node releases its successors by reducing their remaining indegrees; a successor becomes ready when its count reaches zero. For a pure ordering function, processing means adding the node to the output. For an executor, readiness is only permission to dispatch: a dependent task should generally become runnable after its prerequisites complete, not merely after they are scheduled.
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Choose the runtime’s contracts before implementing it
Several behaviors are API decisions rather than consequences of Kahn’s algorithm. Document them so callers know what to expect.
- Edge direction: State explicitly whether an edge points from prerequisite to dependent. The examples here use
prerequisite -> dependent; the graph-run documentation describes dependency-before-dependent ordering. - Invalid input: Decide how to handle duplicate node IDs, unknown dependencies, duplicate edges, and self-edges. Validate these cases before starting work, and report which input is invalid rather than letting malformed counts produce confusing readiness behavior.
- Failure semantics: Decide whether a failed prerequisite blocks its dependents, whether independent branches continue, and whether the final result is fail-fast or aggregates errors. A conservative default is to start a dependent only after all prerequisites succeed, while allowing unrelated work to finish.
- Ready-node ordering: A FIFO queue is simple, but it does not imply a unique topological order. If callers need priority or stable ordering among equally ready tasks, define and implement that policy explicitly.
- Concurrency: Specify a maximum number of active operations independently of the ordering algorithm.
- Cancellation: Define whether cancellation stops future dispatch, signals already-running operations, or both.
Build the graph and its indegrees
Use a registry of task IDs, an adjacency list from each prerequisite to its dependents, and a remaining-indegree count for every node. Perform structural validation before invoking any task. This avoids partially running a graph that turns out to contain a missing dependency or invalid identifier.
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- Register every node. Create one entry per task ID and reject duplicates according to your API’s validation policy.
- Initialize adjacency lists and counts. Give every registered node an empty successor list and an indegree of zero.
- Add each dependency edge. For every
A -> B, verify that both endpoints exist, append B to A’s successor list, and increment B’s indegree. If your input format permits repeated edges, decide whether to reject or deduplicate them before counting. - Seed the ready queue. Add every node with an indegree of zero. The queue now contains tasks that have no prerequisites in this graph.
Schedule ready work without confusing dispatch and completion
A runtime needs to account for both ready tasks and in-flight tasks. Keep a count of active operations, and dispatch from the ready queue only while that count is below the configured concurrency limit. When an operation settles, record its outcome, update the state of its dependents according to your failure policy, and dispatch newly eligible work.
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For a success-only dependency policy, decrement a dependent’s remaining prerequisite count only when its prerequisite succeeds. If a prerequisite fails, mark dependent work as blocked (or propagate a documented failure state) rather than accidentally treating failure as success. Continue independent branches if that is the selected policy. If the API instead treats any settled prerequisite as sufficient, say so clearly: dependents may then run after a failure.
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JavaScript Promise handlers run asynchronously, and MDN notes that “async/await has the same concurrency semantics as normal promise chains.” Awaiting one operation suspends the async function that is awaiting it; other already-dispatched asynchronous operations can continue. This is asynchronous coordination, not automatic parallel CPU execution: a long synchronous task on the browser main thread can still delay input and rendering. See MDN’s guide to using promises and its JavaScript execution model.
Store each task’s result by ID as it completes, so callers can inspect outcomes without relying on completion order. Completion order can differ from topological order whenever independent tasks overlap.
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Detect cycles and blocked nodes
For a pure Kahn traversal, count emitted nodes. If the count is smaller than the number of registered nodes, no complete topological ordering was produced: the graph contains a cycle or nodes are blocked behind one. Do not return the partial output as though it were a valid full order.
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Handle aborts as signals to operations, not magic Promise cancellation
A Promise does not provide a universal cancellation protocol. MDN explains that “Promise itself has no first-class protocol for cancellation, but you may be able to directly cancel the underlying asynchronous operation, typically using AbortController.” Accept an AbortSignal when useful, stop dispatching pending tasks after it fires, and pass the signal to operations that support it. Decide whether active tasks are signalled too; tasks that do not observe the signal may continue.
The graph-run documentation provides an example contract in which pending work is skipped when its supplied signal aborts. Treat that as one possible runtime policy, not as a behavior automatically supplied by Promises. See MDN’s Promise guide for the distinction between Promise settlement and cancellation of an underlying operation.
Test the cases that expose scheduler bugs
Test ordering constraints and runtime behavior separately. A useful test suite includes:
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- A chain such as
A -> B -> C, verifying that each dependent starts only after its prerequisite meets the chosen completion condition. - Two independent nodes, verifying that both can be in flight when the concurrency limit permits it.
- A concurrency cap, verifying that active work never exceeds the configured maximum.
- A graph with several initially ready nodes, verifying the documented tie-breaking behavior without assuming a unique topological order.
- A cycle and a node downstream from that cycle, verifying that incomplete traversal is reported rather than accepted as a full order.
- A task failure, checking whether dependents are blocked and whether unrelated branches continue as promised.
- An abort before dispatch and during active work, checking pending-work and active-operation behavior separately.
- Malformed input, checking duplicate IDs, unknown endpoints, repeated dependencies, and self-edges against the validation contract.
Keep CPU-heavy work off the main thread when it would block browser interactions; an async function does not make synchronous computation non-blocking. For I/O-bound tasks, bounded asynchronous dispatch can improve throughput without changing the dependency constraints.
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